A sample of helium is initially at 605 torr in
a volume of 2.85 L.
At 24.7 °C you found the density of He to
be 0.130 g/L and the density of Ar to be
1.30 g/L even though both samples had
the same number of moles. Which one of
the following best explains why the
densities are different?

Answers

Answer 1

The reason why the densities of helium (He) and argon (Ar) are different despite having the same number of moles is due to their difference in molar mass (molecular weight).

The density of a gas is dependent on its molecular weight.  Even though both samples have the same number of moles, the molecular weight of helium (4 g/mol) is much smaller than that of argon (40 g/mol).

Therefore, the helium sample will have a lower density than the argon sample, even if they are at the same pressure and temperature.

Since density is mass divided by volume, the difference in molar mass results in different densities for the two gases, with helium being less dense than argon.

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Related Questions

write the formulas for the analogous species of the elements of period 3.

Answers

The analogous species of the elements in period 3 can be determined by examining their positions in the periodic table and their similarities in electronic configuration and chemical properties.

Here are the formulas for the analogous species of the elements in period 3:

Sodium (Na) - Analogous Species: Magnesium (Mg)

Formula: Mg

Magnesium (Mg) - Analogous Species: Aluminum (Al)

Formula: Al

Aluminum (Al) - Analogous Species: Silicon (Si)

Formula: Si

Silicon (Si) - Analogous Species: Phosphorus (P)

Formula: P

Phosphorus (P) - Analogous Species: Sulfur (S)

Formula: S

Sulfur (S) - Analogous Species: Chlorine (Cl)

Formula: Cl

Chlorine (Cl) - Analogous Species: Argon (Ar)

Formula: Ar

Each of these analogous species in period 3 exhibits similar electronic configurations and shares some chemical properties.

However, it's important to note that the properties of these elements also vary due to the progressive filling of electron shells and the transition from metals to nonmetals across the period.

Please note that these formulas represent the elemental forms of the analogous species.

The elements can combine with other elements to form various compounds and molecules, resulting in different chemical formulas.

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Write the Longhand and Shorthand Configurations for:

Silver-

Rubidium-

Bromine-

Aluminum-

PLEASE HURRY

Answers

The long hand configuration is the full electronic configuration and the short hand configuration is the noble gas configuration.

1) Silver :

The atomic number of the silver is 47. The long hand configuration is :

=  1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁶ 5s¹ 4d¹⁰

The sort hand configuration is :

= [Kr] 4d¹⁰ 5s¹

2) Rubidium :

The atomic number of the rubidium is 37 . The long hand configuration is :

= 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁶ 5s¹

The sort hand configuration is :

= [Kr] 5s¹

3) Bromine :

The atomic number of the bromine is 35. The long hand configuration is :

= 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁵

The sort hand configuration is :

= [Ar] 4s² 3d¹⁰ 4p⁵

4) Aluminum :

The atomic number of the aluminum is 13. The long hand configuration is :

= 1s² 2s² 2p⁶ 3s² 3p¹

The sort hand configuration is :

= [Ne] 3s² 3p¹

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Which of the following represents the number of Molecules of the type indicated is present as a reactant or product of the chemical reaction shown?

Answers

Following represents the number of Molecules of the type indicated is present as a reactant or product of the chemical reaction shown is the coefficient of the species

The number of atoms, molecules, or formula units of a reactant or product in a balanced chemical equation is the coefficient of that species then the mole ratio of two substances in a chemical reaction is the ratio of their coefficients in the balanced chemical equation and the this numbers are called as coefficient and they tell how many of each molecule are participate in the reaction

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The equilibrium concentrations for the reaction between N2 and O2 to form NO at a certain temperature are given in the table below. What is the equilibrium constant for the reaction?

A. 42

B. 2.4 x 10^-2

C. 4.2 x 10^-4

D. 21

The equilibrium concentrations for the reaction between N2 and O2 to form NO at a certain temperature

Answers

Answer:

c

Explanation:

c is correct i believe

icl(g) cl₂(g) → icl₃(s). the ∆g° of the reaction is -17.09 kj/mol. calculate the keq for the reaction at 298.0 k.

Answers

To calculate the equilibrium constant (K_eq) for the reaction at 298.0 K, we can use the relationship between the standard Gibbs free energy change (∆G°) and the equilibrium constant.

∆G° = -RT ln(K_eq) Where:

∆G° is the standard Gibbs free energy change (-17.09 kJ/mol)

R is the gas constant (8.314 J/(mol·K)) (note the units)

T is the temperature in Kelvin (298.0 K)

ln denotes the natural logarithm

First, we need to convert the given ∆G° value from kJ/mol to J/mol:

∆G° = -17.09 kJ/mol × 1000 J/kJ = -17090 J/mol

Now we can calculate the equilibrium constant:

∆G° = -RT ln(K_eq)

K_eq = e^(-∆G° / (RT))

Plugging in the values:  K_eq = e^(-(-17090 J/mol) / ((8.314 J/(mol·K)) × 298.0 K))

K_eq = e^(17090 / (8.314 × 298.0))

Calculating the expression inside the exponent:

K_eq = e^(72.718)

K_eq ≈ 1.689 × 10^31

Therefore, the equilibrium constant (K_eq) for the given reaction at 298.0 K is approximately 1.689 × 10^31.

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Can someone please explain to me how I’m supposed to figure out the element with these configurations??

Can someone please explain to me how Im supposed to figure out the element with these configurations??

Answers

11. Sulfur
12. Boron
13.Strontium
14. Hydrogen
15 and 16. Potassium
If you google electron configurations periodic table you can see all the orbital and sub levels types and you just simply count until you reach the end of the configuration given.

aluminum hydroxide + sodium nitrate reaction type

Answers

Answer:

.

Explanation:

Write balanced, net ionic equations for the reactions shown below. Identify the spectator ions. (40
points possible: 8 points per problem = 4 points for net ionic equation, 4 points for spectator ions)
a. Sr(NO3)2 (aq) + H2SO4 (aq) → SrSO4 (s) + 2HNO3 (aq)

Answers

Taking into account the definition of net ionic equation, the net ionic equation is Sr²⁺(aq) + 2 SO₄⁻(aq) → SrSO₄ (s) and H⁺ and NO₃⁻ are the spectator ions.

The net ionic equation is a chemical equation for a reaction that lists only the species that participate in the reaction.

In other words, an ionic equation is a chemical equation where electrolytes in aqueous solution are written as dissociated ions. Usually this is a salt dissolved in water, where the ionic species are followed by (aq) in the equation, to indicate that they are in aqueous solution.

The balanced equation will be:

Sr(NO₃)₂ (aq) + H₂SO₄ (aq) → SrSO₄ (s) + 2 HNO₃ (aq)

where (aq) means aqueous and (s) solid.

Taking into account that:

All salts of NO₃⁻, C₂H₃O₂⁻, ClO₃⁻ and ClO₄⁻ are soluble.

The total ionic equation in separated aqueous solution will be:

Sr²⁺(aq) + 2 NO₃⁻(aq) + 2 H⁺(aq) + 2 SO₄⁻(aq) → SrSO₄ (s) + 2 NO₃⁻(aq) + 2 H⁺(aq)

A spectator ion is an ion that appears both as a reactant and as a product in an ionic equation.

Spectator ions can be either cations (positively charged ions) or anions (negatively charged ions).

When writing a net ionic equation, spectator ions found in the original equation are ignored. Thus, the total ionic reaction is different from the net chemical reaction.

In this case, H⁺ and NO₃⁻ are the spectator ions because they appear unchanged in both the product and the reagent. So these ions cancel out by writing the net ionic equation and you get:

Sr²⁺(aq) + 2 SO₄⁻(aq) → SrSO₄ (s)

In summary, the net ionic equation is Sr²⁺(aq) + 2 SO₄⁻(aq) → SrSO₄ (s) and H⁺ and NO₃⁻ are the spectator ions.

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Convert each of the following lengths to the units requested.
a. 17.3 m to centimeters





b. 2.56 m to kilometers





567 dm to meters




5.13 m to millimeters

Answers

Answer:

1730 cm

0.00256 km

5130 mm

The nucleus contains positively charged ___ and neutral ___ and makes up more than 99% of the mass of an atom.

Answers

Answer:

ions

Explanation:

atoms because of the charge

Why is there no liquid metallic hydrogen zone in the interiors of uranus or neptune?.

Answers

Two answers. Pressure and they're not big enough.

Now, you see, in order for hydrogen to be metallic, the interiors of Uranus and Neptune would have to have more pressure.

Pressure can be defined as the exertion of force upon a surface by an object, fluid, etc., in contact with it.

The three states of matter on Earth are solid, liquid, and gas. An element's shape is determined by its temperature and pressure. On Earth, hydrogen is generally a gas, but it may be intentionally cooled and compressed to change its state into a liquid or a solid. Hydrogen is still a non-metal even in these states; since its atoms strongly cling on to their electrons, it has poor electrical and thermal conductivity. Contrarily, metals have good electrical and thermal conductivity due to the arrangement of their atoms, which forms a lattice that makes it simple for the outermost electrons of one atom to go to another.

Jupiter and Saturn are the two gas giants in our solar system. Based on their densities, both planets have a considerable amount of hydrogen in them. However, the hydrogen in these giants is heated and compressed to such high temperatures and pressures that it assumes a number of peculiar phases, including liquid metallic hydrogen. Hydrogen, as I previously stated, is a non-metal. However, in Jupiter and Saturn, the extreme temperatures and pressures cause hydrogen atoms to lose their electrons, resulting in a stew of free-floating hydrogen nuclei (protons) and electrons. The ability of the electrons to travel freely between the nuclei due to their unbound state is a characteristic of metals. This is metallic hydrogen, which has a metallic-like behavior. Metallic hydrogen is conductive and is thought to play a significant role in the dynamo that drives the magnetic fields of Jupiter and Saturn. (However, the dynamo on Earth is propelled by liquid iron, a real metal.)

The ice giants of our solar system, Uranus and Neptune, are too dense for hydrogen to make up a significant portion of their composition. In addition, because of how similar their masses are, planetary scientists presume that the innards of these two planets are comparable and that hydrogen makes up just around 15% of their masses. Although hydrogen is thought to form a liquid molecular shell deeper into Uranus and Neptune and is present in their atmospheres, it never experiences the pressures and temperatures necessary to transform into metallic hydrogen.

Thanks.

What are the three things that is needed for precipitation to form? Water vapor Lifting action Freezing temperatures Convective turning Growth process Steady rotation of wind

Answers

The three things that are needed for precipitation to form are water vapor, lifting action, and freezing temperatures. When warm moist air is lifted, it cools and condenses into clouds.

If the air continues to cool and the temperature drops below freezing, the water droplets freeze and become ice crystals.

These ice crystals then collide and merge with other ice crystals, forming larger snowflakes or hailstones. Finally, when these snowflakes or hailstones become too heavy to be supported by the updrafts in the cloud, they fall to the ground as precipitation.

Additional terms such as convective turning, growth process, and steady rotation of wind may also contribute to the formation of precipitation in certain weather conditions.

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How many grams of ammonia are needed to make 1.25 L solution with a pH of 11.68?​

Answers

The mass (in grams) of ammonia, NH₃ needed to make 1.25 L solution with a pH of 11.68 is 0.102 grams

How do i determine the mass of ammonia needed?

First, we shall determine the hydroxide ion concentration in the solution. Details below:

pH of solution = 11.68pOH = 14 - 11.68 = 2.32Hydroxide ion concentration [OH⁻] =?

pH of a solution is given by the following formula:

pOH = -Log  [OH⁻]

Inputting the various parameters, we have

2.32 = -Log  [OH⁻]

Multiply through by -1

-2.32 = Log [OH⁻]

Take the anti-log of -2.32

[OH⁻] = Anti-log -2.32

[OH⁻] = 0.0048 M

Next, we shall determine the molarity of the ammonia. Details below:

NH₃(aq) + H₂O <=> NH₄⁺(aq) + OH⁻(aq)

From the above equation,

1 mole of OH⁻ is present in 1 mole of NH₃

Therefore,

0.0048 M OH⁻ will also be present in 0.0048 M NH₃

Next, we shall determine the mole of ammonia. Details below:

Volume = 1.25 LMolarity = 0.0048 MMole of ammonia =?

Molarity = Mole / Volume

Cross multiply

Mole of ammonia = molarity × volume

Mole of ammonia = 0.0048 × 1.25

Mole of ammonia = 0.006 mole

Finally, we shall determine the mass of ammonia needed. Details below:

Mole of ammonia = 0.006 moleMolar mass of ammonia = 17 g/molMass of ammonia = ?

Mass = Mole × molar mass

Mass of ammonia = 0.006 × 17

Mass of ammonia = 0.102 grams

Therefore, the mass of ammonia needed is 0.102 grams

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using the reagents below, list in order (by letter, no period) those necessary to transform 1-chlorobutane into 1-butyne.

Answers

The reagents necessary to transform 1-chlorobutane into 1-butyne are as follows: Sodium amide (NaNH2) ,Liquid ammonia (NH3) ,Acetylene , (ethyne, C2H2) ,Sodium metal (Na) , Absolute ethanol (C2H5OH)

The conversion of 1-chlorobutane (C4H9Cl) to 1-butyne (C4H6) involves a series of reactions. Here is the step-by-step process:

Step 1: Conversion of 1-chlorobutane to 1-butene

1-chlorobutane (C4H9Cl) reacts with sodium amide (NaNH2) and liquid ammonia (NH3) to form 1-butene (C4H8) and sodium chloride (NaCl):

C4H9Cl + NaNH2 → C4H8 + NaCl + NH3

Step 2: Conversion of 1-butene to butyne

1-butene (C4H8) is reacted with acetylene (C2H2) in the presence of sodium metal (Na) as a catalyst, resulting in the formation of 1-butyne (C4H6):

2 C4H8 + 5 C2H2 → 4 C4H6

Step 3: Purification

The resulting mixture of products is subjected to purification by distillation or other suitable methods to isolate 1-butyne.

To transform 1-chlorobutane into 1-butyne, the reagents needed are sodium amide (NaNH2), liquid ammonia (NH3), acetylene (C2H2), sodium metal (Na), and absolute ethanol (C2H5OH) as a solvent. The process involves the conversion of 1-chlorobutane to 1-butene using sodium amide and liquid ammonia, followed by the reaction of 1-butene with acetylene in the presence of sodium metal to obtain 1-butyne. The final product, 1-butyne, can then be purified to obtain a pure sample.

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Which electron configuration is correct for a ca 2 ion?
a. 1s22s22p63s23p1
b. 1s22s22p63s23p64s24p6
c. 1s22s22p63s23p64s2
d. 1s22s22p63s2
e. 1s22s22p63s23p6

Answers

The correct answer for electron configuration of a Ca2+ ion is e. 1s22s22p63s23p6 which is isoelectronic with the noble gas argon.

Isoelectronicity is a phenomenon determined whilst or greater molecules have equal structure (positions and connectivities amongst atoms) and equal digital configurations, however, range through what particular factors are at positive places withinside the structure.

This definition is on occasion termed valence isoelectronic. Definitions can on occasion be now no longer as strict, on occasion requiring identification of the full electron matter and with it the whole digital configuration.[2] More usually, definitions are broader and can enlarge to permit one-of-a-kind numbers of atoms withinside the species being compared.[3]

The significance of the idea lies in figuring out considerably associated species, as pairs or series. Isoelectronic species may be anticipated to reveal beneficial consistency and predictability of their houses, so figuring out a compound as isoelectronic with one already characterized gives clues to feasible houses and reactions (Differences in houses which includes electronegativity of the atoms in isoelectronic species can have an effect on reactivity.)

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what will be the result of the reaction
(CH3COO)2+redP +Cl2

Answers

Answer:

(CH3COO)2 + redP + Cl2 → ClCH2COOH + HCl

Explanation:

This is an example of halogenation of carboxylic acids at alpha carbon atom. In this reaction, red phosphorus and chlorine are treated with carboxylic acids having alpha hydrogen atom followed by hydrolysis to form alpha chloro carboxylic acid.

How much of each of the following substances would you add to water to prepare 1.50 l of a 0.60 m solution?

Answers

From concentrated (18 M) sulfuric acid [H2SO4]

To prepare the solution, we dilute 33 mL of 18 M sulfuric acid to 1.00 L.

Molarity (M) = moles solute / Liter solution  

Mass%  = mass solute / mass solution×100

We can calculate the amount of 18 M sulfuric acid that needs to be diluted to 1.000 L from a concentrated solution using the dilution method. When determining the volume of 18 M sulfuric acid required, we arrive at

      V1C1 = V2C2

      V1 = (0.60M H2SO4) (1L) / (18M H2SO4)

      V1 = 0.033L = 33mL

To prepare the solution, we dilute 33 mL of 18 M sulfuric acid to 1.00 L.

A substance's molarity (M) is the volume of solution in which it is present. The amount of a solute in moles per liter of a solution is known as molarity. A solution's molar concentration is another name for molarity.

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is adding hydrochloric acid to milk a physical or chemical change?

Answers

answer: operating machines they are easy to handle

What type of particle reinforced composite has extremely small particles?

Answers

Answer:

large particle composite

What does a Primary Consumer eat?

Answers

Plants or algae, they are herbivores

Please i need help with this question.
Please show workings where necessary and proof/ explain your point​

Please i need help with this question.Please show workings where necessary and proof/ explain your point

Answers

Answer:

C

Explanation:

Please see the attached picture for the explanation.

Le Châtelier's principle:

When a stress is applied to a system at equilibrium, the system will respond by shifting in the direction that opposes/ minimizes the effect of the stress.

• This stress could be the addition or removal of a product or reactant, changes in the concentration of the products or reactants, or a change in temperature.

☆ Why can heat be written on the same side of the products when the reaction is exothermic?

• Exothermic means that heat is released, thus heat can be treated as a product.

• I like to remember it as Exothermic → Exit

Please i need help with this question.Please show workings where necessary and proof/ explain your point

if u could buy 500 individual nerds candies for $5 or 186 g of individual nerds candies for 5, which would be better ? why?

Answers

Answer: 500 individual nerds candies for $5 would be better bc u would have more candy and it would last a while

Explanation: would have more candies

To solve this we must be knowing each and every concept related to division. Therefore, 500 individual nerds candy for $5 is preferable since you will have more candy and it will last longer.

What is division?

Division is one of four fundamental mathematical operations, the others being addition, subtraction, and multiplication. Division is defined as the equal division of larger groups into smaller units.

The division of labor is the sequence of tasks given to and performed by the  group of staff in order to maximize efficiency. The splitting down of a job into multiple separate parts that make up the total is referred to as division of labor. 500 individual nerds candy for $5 is preferable since you will have more candy and it will last longer.

Therefore, 500 individual nerds candy for $5 is preferable since you will have more candy and it will last longer.

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IWhich of the following solutions would be most likely to have the highest water concentration?

Multiple Choice hypertonic solution isotonic solution hypotonic solution water concentration and tonicity of a solution cannot be compared

Answers

"Hypotonic solution," refers to a solution with the highest water concentration due to its lower solute concentration compared to the other options, leading to water influx into cells.

A hypotonic solution would be most likely to have the highest water concentration. In a hypotonic solution, the solute concentration is lower than that inside the cell or compared to another solution. As a result, water tends to move into the cell or the solution to equalize the concentration.

When a cell is placed in a hypotonic solution, water molecules will move into the cell through the process of osmosis. This influx of water increases the water concentration inside the cell, leading to cell swelling or even bursting in extreme cases.

Compared to hypertonic and isotonic solutions, a hypotonic solution has a lower solute concentration, allowing for a higher concentration of water molecules. This results in a higher water concentration in the solution. It's important to note that the concept of tonicity is related to the relative solute concentrations between two solutions and their effect on cell osmosis. In this case, a hypotonic solution is characterized by a higher water concentration compared to the other options.

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When an ionic bond forms what type of ions are joined?

Answers

It usually becomes a positive ion, or cation.

Which of these characteristics will produce the most water dense water

Answers

Answer:

High salinity, low temperature.

Explanation:

A lot of salt is left behind. This leads to water with  very high salinity

The salinity of the water increases as more salt is dissolved in it. High temperature, density and salinity produce the most dense water.

What is salinity of water ?

Salinity influences the physical properties of water, such as density and heat capacity, together with temperature and pressure.

When two water samples of the same volume are compared, the water sample with the higher salinity will have more mass and be more dense.

The ocean's salinity is raised by both sea ice production and ocean water evaporation. However, processes that reduce salinity, such as the ongoing inflow of fresh water from rivers, precipitation of rain and snow, and melting of ice, constantly balance out these "salinity rising" causes.

Thus, salinity ,density and high temperature produce the water dense.

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How do you find the number of neutrons for any atom?

Answers

The number of neutrons is equal to the difference between the mass number of the atom and the atomic number.

Put in order:
(a) produce carbon dioxide and molten iron
(b) pour off molten iron
(c) mix with limestone and coal
(d) place in blast furnace

Answers

In order to produce molten iron and carbon dioxide in a blast furnace, the following steps are typically taken:

Place limestone, coal, and iron ore in a blast furnace. (c)

Heat the blast furnace to high temperatures, causing the limestone to break down and release carbon dioxide. (d)

The carbon dioxide reacts with the coal to produce carbon monoxide, which then reacts with the iron ore to reduce it to molten iron. (a)

Pour off the molten iron from the bottom of the blast furnace. (b)

These steps are part of the process of producing iron in a blast furnace, which is a common method used in the production of steel and other iron-based products. It is important to follow proper procedures and safety protocols when working with blast furnaces, as they involve high temperatures and potentially hazardous materials.

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If the spring constant is 12.6N/m and a spring is stretched by 0.25m, how much force has been applied?

Answers

Answer:

3.15N

Explanation:

We use this equation:

F= k∆x

Where ∆x refers to the amount or stretch or compression and k is the spring constant.

F = force

k = spring constant

∆x = change in length of spring

To find the value of F:

F= k∆x

F= 12.6x0.25

F= 3.15N

(1) What is the element with an electron configuration of 1s22s22p63s23p64s23d6?

(2) What is the element with an electron configuration of 1s22s22p63s23p6?
(3) What is the name of the element with a valence electron configuration of 4s1?


(4) What is the name of the element with a valence electron configuration of 2s22p5?

A. An element with the valence electron configuration 3s1 would form a monatomic ion with a charge of .
In order to form this ion, the element will (lose or gain) (1/2/3/4/5/6/7/8) electron(s) from/into the ( s/p/d/f/ s + p /s + d/ p + d) subshell(s).


B. An element with the valence electron configuration 3s23p3 would form a monatomic ion with a charge of .
In order to form this ion, the element will (lose or gain) (1/2/3/4/5/6/7/8) electron(s) from/into the( s/p/d/f/ s + p /s + d/ p + d) subshell(s).

Answers

(1) The element with an electron configuration of    1s22s22p63s23p64s23d6 is Iron (Fe).

The above electronic configuration is the repesentation of the electrons presents in different orbitals of the iron(Fe) .we have seen that all orbitals is completely filled before D orbital.

(2) The element with an electron configuration of 1s22s22p63s23p6 is Argon (Ar)

The above electronic configuration is the repesentation of the electrons presents in different orbitals of the Argon(Ar) .we have seen that all orbitals  is completely filled.

(3) The name of the element with a valence electron configuration of 4s1 is Potassium (K)

The above electronic configuration is the repesentation of the electrons presents in different orbitals of thePotassium (K) .we have seen that all orbitals  is completely filled before  4s1.

(4) The name of the element with a valence electron configuration of 2s22p5 is Flourine (F)

The above electronic configuration is the repesentation of the electrons presents in different orbitals of the Flourine (F) .we have seen that all orbitals  is completely filled before  2p5.

A. An element with the valence electron configuration 3s1 would form a monatomic ion with a charge of +1. In order to form this ion, the element will lose one electron from the 3s subshell.

B. An element with the valence electron configuration 3s23p3 would form a triatomic ion with a charge of -3. In order to form this ion, the element will gain three electrons from the 3s and 3p subshells.

Elements achieve an inert gas configuration by gaining or losing electrons to attain a full valence shell of electrons, resulting in a stable electron configuration. This is also known as having a complete octet in their outermost energy level.

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Determinar el valor positivo de “m” para que la ecuación: x(x+2)=4mx−8 ; tenga una raíz que sea el doble de la otra.

Answers

El valor positivo de \(m\) para que la ecuación \(x\cdot (x+2) = 4\cdot m \cdot x - 8\) tenga una raíz que sea el doble de la otra es 2.

De acuerdo con el enunciado de esta pregunta, debemos encontrar un valor de \(m\) a partir del siguiente sistema de ecuaciones:

\(r\cdot (r+2) = 4\cdot m \cdot r -8\) (1)

\(2\cdot r \cdot (2\cdot r + 2) = 4\cdot m \cdot (2\cdot r) - 8\) (2)

Ahora simplificamos el sistema de ecuaciones:

\(r^{2}+2\cdot r = 4\cdot m\cdot r - 8\) (1b)

\(4\cdot r^{2}+4\cdot r =8\cdot m\cdot r - 8\) (2b)

Despejamos \(m\) en cada expresión, lo eliminamos y resolvemos el polinomio resultante:

\(\frac{r^{2}+2\cdot r + 8}{4\cdot r} = \frac{4\cdot r^{2}+4\cdot r +8}{8\cdot r}\)

\(r^{2}+2\cdot r + 8 = 2\cdot r^{2}+2\cdot r +4\)

\(r^{2}-4 = 0\)

\(r^{2} = 4\)

\(r = \pm 2\)

Finalmente, determinamos el valor de \(m\), que al ser positivo, debemos utilizar \(r = 2\):

\(m = \frac{2^{2}+2\cdot 2 + 8}{4\cdot 2}\)

\(m = 2\)

El valor positivo de \(m\) para que la ecuación \(x\cdot (x+2) = 4\cdot m \cdot x - 8\) tenga una raíz que sea el doble de la otra es 2.

Invitamos cordialmente a ver esta pregunta sobre polinomios de segundo orden: https://brainly.com/question/15792293

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