Question

Calculate the molar mass of a gas if 2.50 g occupies 0.865 dm3 at 87.3 kPa and 31 ∘C

Answer 1

Answer

Step 1: Explanation:

We know the ideal gas equation,

PV=nRT

where,

R=universal gas constant, T=temperature ,

P=pressure ,V= volume, n=moles.

We know also know that

moles(n) = mass(w) / molar mass (M)

hence, the equation becomes

=====> PV=nRT

or ,   PV= (w/M) RT

or, M= wRT / PV

Step 2: Extract the data from question

Given,

pressure = 87.3 kPa = 0.861584

[ note: 1 atm equals to 101.325 kPa => 87.3 kPa × (1 atm / 101.325 kPa ) = 0.861584 atm

Temperature = 31°C = ( 31 +273.15 ) K = 304.15 K

Volume = 0.865 dm3 = 0.865 L [ because 1 dm3 = 1 L ]

Mass ( w) = 2.50 g

Step 3: Calculate the molar mass

substitute the above value in equation

M= wRT / PV

M =   (2.50 g  × 0.08206 L-atm mol-1K-1 × 304.15 K ) / ( 0.861584 atm × 0.865 L )

M = 83.72 g / mol

hence, the molar mass of the gas is 83.72 g/mol