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Density

At 25∘𝐶 and ...

Question

At $25^{\circ} C$ and $760 m m$ of $H g$ pressure a gas occupies $600 m L$ volume. What will be its pressure at a height where temperature is $10^{\circ} C$ and volume of the gas is $640 m L .$

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Solution

Pressure of gas

Given: $P_{1} = 760 m m H g, V_{1} = 600 m L, T_{1} = 25^{\circ} C = 298 K$
and $V_{2} = 640 m L, T_{2} = 10^{\circ} C = 283 K$

According to Combined gas law, $P V \propto T$

So, $\begin{matrix} \frac{P_{1} V_{1}}{T_{1}} & = \frac{P_{2} V_{2}}{T_{2}} \Rightarrow P_{2} & = \frac{P_{1} V_{1} T_{2}}{T_{1} V_{2}} \Rightarrow P_{2} & = \frac{(760 m m H g) \times (600 m K) \times (283 K)}{(640 m L) \times (298 K)} = 676.6 m m H g \end{matrix}$

Final answer:

Pressure of the gas is $676.6 m m H g .$

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