# Chem Problem: density of a gas of unknown molar mass was measured as a function of pressure at 0,Determine a precise molar mass for the gas.?

The density of a gas of unknown molar mass was measured as a function of pressure at 0 ∘C, as in the table below.

1. Determine a precise molar mass for the gas. Hint: Graph d/P versus P.

2. Why is d/P not a constant as a function of pressure?

### 1 Answer

- Dr WLv 74 weeks ago
plot d/P vs P???

here's how I would do it

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starting with these 2 equations

.. PV = nRT.. .. . ... ideal gas law

.. mw = mass / n.. . definition of molar mass (mw)

subbing and rearranging

.. PV = (mass / mw) RT

.. P = (RT/mw) * (mass / V)

since density (ρ) = mass / V

.. P = (RT/mw) * ρ

that's a linear equation if we plot P vs ρ slope = RT/mw

see the attached plot

and we know slope = RT/mw so that

.. RT/mw = 0.4354 atm/(g/L) = 0.4354 Latm / g

.. mw = RT * (1g / 0.4354 Latm)

.. mw = 0.08206 Latm/molK * 273.15K * (1g / 0.4354Latm) = 51.48g/mol