Question

In constant volume, container of 0.82 litre, log P vs log T is plotted as shown in graph. Calc number of moles of ideal gas present in container:

Answer 1

100

Answer 2

The ideal gas law is $PV = nRT$. Since the volume (V) is constant, we can rearrange the equation to $P = \frac{nR}{V}T$. Taking the logarithm of both sides, we get $\log P = \log(\frac{nR}{V}) + \log T$. This equation is in the form of a straight line $y = mx + c$, where $y = \log P$, $x = \log T$, the slope $m=1$, and the y-intercept $c = \log(\frac{nR}{V})$. From the graph, the y-intercept is given as 1. Therefore, $\log(\frac{nR}{V}) = 1$, which implies $\frac{nR}{V} = 10^1 = 10$. Given $V = 0.82$ litre and using the ideal gas constant $R = 0.0821$ L atm/(mol K), we can solve for the number of moles (n): $n = \frac{10 \times V}{R} = \frac{10 \times 0.82 \text{ L}}{0.0821 \text{ L atm / (mol K)}} = \frac{8.2}{0.0821} \text{ mol} = 100 \text{ mol}$.