Chemistry, 25.07.2019 14:00 brianortega1208

The density of a gas is measured at 1.653 g/l at 746 mmhg and 25.0 °c. what is its molar mass?

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Answer from: daydallas01

The molar mass of gas is $\boxed{{\text{41}}{\text{.22 g/mol}}}$ .

Further Explanation:

An ideal gas is a hypothetical gas that is composed of a large number of randomly moving particles that are supposed to have perfectly elastic collisions among themselves. It is just a theoretical concept and practically no such gas exists. But gases tend to behave almost ideally at a higher temperature and lower pressure.

Ideal gas law is the equation of state for any hypothetical gas. The expression for the ideal gas equation is as follows:

${\text{PV}} = {\text{nRT}}$ …… (1)

Here,

P is the pressure of the ideal gas.

V is the volume of the ideal gas.

T is the absolute temperature of the ideal gas.

n is the number of moles of gas.

R is the universal gas constant.

The formula to calculate the number of moles of gas is as follows:

${\text{n}} = \frac{{\text{m}}}{{\text{M}}}$ ...... (2)

Here,

n is the number of moles of gas.

m is the mass of gas.

M is the molar mass of gas.

The formula to calculate the density of the gas is as follows:

${\rho }} = \frac{m}{V}$ ...... (3)

Here,

${\rho }}$ is the density of the gas.

m is the mass of gas.

V is the volume of gas.

Rearrange equation (3) to calculate the mass of gas.

${\text{m}}={\rho V}}$ ...... (4)

Substitute the value of mass from equation (4) in equation (2).

${\text{n}} = \frac{\rho V}{{M}}}$ ...... (5)

Substitute the value of n from equation (5) in equation (1).

${\text{P}} = \frac{\rho RT}{{\text{M}}}$ ...... (6)

Rearrange equation (6) to calculate M.

${\text{M}} = \frac{\rho RT}{{\text{P}}}$ ...... (7)

The density of the gas is 1.653 g/mL.

The pressure of the ideal gas is 746 mm Hg.

The temperature of the ideal gas is ${\text{25}}\;^\circ {\text{C}}$ .

The universal gas constant is 0.0821 L atm/K mol.

Substitute these values in equation (7).

$\begin{aligned}{\text{M}}&=\frac{{\left({{\text{1}}{\text{.653 g/mL}}}\right)\left( {0.0821{\text{ L atm/K mol}}}\right)\left({25+27{\text{3}}{\text{.15}}}\right){\text{K}}}}{{\left( {746{\text{ mm Hg}}}\right)\left({\frac{{{\text{1 atm}}}}{{760{\text{ mm Hg}}}}} \right)}} \\&=41.2{\text{216 g/mol}}\\&\approx {\text{41}}{\text{.22 g/mol}}\\\end{aligned}$

Learn more:

1. How many moles of Cl are present in 8 moles of ${\text{CC}}{{\text{l}}_4}$ ?

2. Calculate the moles of ions in HCl solution:

Answer details:

Grade: Senior School

Subject: Chemistry

Chapter: Mole concept

Keywords: P, V, n, R, T, ideal gas, pressure, volume, 41.22 g/mol, density, molar mass, 1.653 g/mL, 746 mm Hg, m, M.

Answer from: Quest

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Answer from: Quest

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