(a) Show that the density of an ideal gas occupying a volume V is given by $p = P M / R T$ , where M is the molar mass. (b) Determine the density of oxygen gas at atmospheric pressure and ${20.0}^{0} C$ .

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Solution

(a) Let m represent the sample mass.
The number of moles is $n = \frac{m}{M}$
and the density is $p = \frac{m}{V}$ .
So $P V = n R T$ becomes $P V = \frac{m}{M} R T$ or $P M = \frac{m}{V} R T$ .
Then, $p = \frac{m}{V} \frac{P M}{R T}$
(b) $p = \frac{P M}{R T} = \frac{(1.013 \times 10^{5} N / m^{2}) (0.032 0 k g / m o l)}{(8.314 J / m o l . K) (293 K)} = 1.33 k g / m^{3}$

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(a) Show that the density of an ideal gas occupying a volume V is given by p=PM/RT, where M is the molar mass. (b) Determine the density of oxygen gas at atmospheric pressure and 20.00C.

(a) Let m represent the sample mass. The number of moles is n=mM and the density is p=mV .So PV=nRT becomes PV=mMRT orPM=mVRT. Then, p=mVPMRT (b) p=PMRT=(1.013×105N/m2)(0.0320kg/mol)(8.314J/mol.K)(293K)=1.33kg/m3

(a) Show that the density of an ideal gas occupying a volume V is given by $p = P M / R T$ , where M is the molar mass. (b) Determine the density of oxygen gas at atmospheric pressure and ${20.0}^{0} C$ .