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Ideal Gas Equation

Under the ide...

Question

Under the identical conditions of temperature, the density of a gas $X$ is two times to that of gas $Y$ while the molecular mass of gas $Y$ is three times that of $X$ . The ratio of pressure of $X$ and $Y$ is $a : b$ . Then $a + b$ is:

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Solution

According to ideal gas equation: $P V = n R T$
Ratio of pressure,
$\frac{p_{1}}{p_{2}} = \frac{(m_{1} / V_{1}) R T}{M_{1}} \times \frac{1}{\frac{(m_{2} / V_{2}) R T}{M_{2}}} = \frac{(d_{1}) R T}{M_{1}} \times \frac{1}{\frac{(d_{2}) R T}{M_{2}}} = \frac{(2 d_{2}) R T}{M_{1}} \times \frac{1}{\frac{(d_{2}) R T}{3 M_{1}}} = 6 : 1 = a : b$ .
Now,

$a + b = 6 + 1 = 7$

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