Question

What is the molar mass of a 3.228 g sample of a gas if it occupies 3.21 L at 298 K and 1.25 atm?

Answer 1

Taking into account the ideal gas law and the definition of molar mass, the molar mass of a 3.228 g sample of a gas if it occupies 3.21 L at 298 K and 1.25 atm is 19.66 $\frac{g}{moles}$.

What is ideal gas law

An ideal gas is a theoretical gas that is considered to be composed of randomly moving point particles that do not interact with each other. Gases in general are ideal when they are at high temperatures and low pressures.

The pressure, P, the temperature, T, and the volume, V, of an ideal gas, are related by a simple formula called the ideal gas law:

P×V = n×R×T

where P is the gas pressure, V is the volume that occupies, T is its temperature, R is the ideal gas constant, and n is the number of moles of the gas. The universal constant of ideal gases R has the same value for all gaseous substances.

Definition of molar mass

The molar mass of substance is a property defined as its mass per unit quantity of substance, in other words, molar mass is the amount of mass that a substance contains in one mole.

Number of moles in this case

In this case, you know:

• P= 1.25 atm
• V= 3.21 L
• n= ?
• R= 0.082 $\frac{atmL}{mol K}$
• T= 298 K

Replacing in the ideal gas law:

1.25 atm× 3.21 L = n× 0.082 $\frac{atmL}{mol K}$× 298 K

Solving:

n= (1.25 atm× 3.21 L)÷ (0.082 $\frac{atmL}{mol K}$× 298 K)

n= 0.1642 moles

So, the number of moles in this case are 0.1642 moles.

Molar mass of the sample

In this case, you know:

• mass= 3.228 g
• number of moles= 0.1642 moles

Then, considering the definition of molar mass, it is calculated as:

$molar mass=\frac{3.228 g}{0.1642 moles}$

Solving:

molar mass= 19.66$\frac{g}{moles}$

Finally, the molar mass of a 3.228 g sample of a gas if it occupies 3.21 L at 298 K and 1.25 atm is 19.66 $\frac{g}{moles}$.

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