Question

what mass of helium (in g) does the balloon contain? 11.45 a 1.007 g sample of an unknown gas exerts a pressure of 95.3 kpa in a 0.452 l container at 23 °c. what is the molar mass of the gas?

Explanation:

Step1: Convert temperature to Kelvin

$T=(23 + 273.15)\text{ K}=296.15\text{ K}$

Step2: Use the ideal - gas law $PV = nRT$ to find the number of moles $n$

$P = 95.3\text{ kPa}=95300\text{ Pa}$, $V = 0.452\text{ L}=0.452\times10^{- 3}\text{ m}^3$, $R = 8.314\text{ J/(mol}\cdot\text{K})$
$n=\frac{PV}{RT}=\frac{95300\text{ Pa}\times0.452\times10^{-3}\text{ m}^3}{8.314\text{ J/(mol}\cdot\text{K})\times296.15\text{ K}}$
$n=\frac{95300\times0.452\times10^{-3}}{8.314\times296.15}\text{ mol}\approx0.0177\text{ mol}$

Step3: Calculate the molar mass $M$

$M=\frac{m}{n}$, where $m = 1.007\text{ g}$ and $n = 0.0177\text{ mol}$
$M=\frac{1.007\text{ g}}{0.0177\text{ mol}}\approx56.9\text{ g/mol}$

Answer:

The molar mass of the gas is approximately $56.9\text{ g/mol}$