The density of a gas is measured at 1.653 g/L at 746 mmHg and 25.0 °C. What is its molar mass?

P M = d R T where;

P: pressure = 746/760 = 0.982 atm

M : Molar mass (unknown)

d: density = 1.653 g / L

R: gas constant = 0.08205 atm. L / mol. K

T: absolute temperature = 25 + 273 = 298 K

M = d R T / P

= (1.653 * 0.08205 * 298) / 0.982 = 41.18 g/mol

Given,

Density of gas = 1.653 g/L

Pressure = 746 mm Hg = 0.981 atm

Temperature = 25 degree Celsius or 298 Kelvin

By ideal gas law we know,

PV=nRT

where,

P=Pressure

V=Volume of gas

n = no. of moles

R=Universal gas constant (0.0821)

T = temperature

Now to know the molar mass, we can use following formula;

Molar mass (M) = mass (m) / no. of moles (n)

or, No. of moles (n) = mass (m) / Molar mass (M)

also, density is related to mass by formula;

Density = Mass (m) * Volume (V)

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Using the above relationship in ideal gas equation, we have,

P. V = m/M. R. T

P. V. M = mRT

M = m / V * RT/P

Since density = m/V, using the relation we get,

M = Density * RT/P

M = (1.653 g/L * 0.082 atm. L/mol. k * 298K) / 0.981 atm

= 41.22 g/mol

Hence the molar mass of the gas is 41.22 g/mol