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Gases

The volume of...

Question

The volume of gas A is twice than of gas B. The compressibility factor of gas A is thrice than that of gas B at same temperature. The pressure of the gases for equal number of moles are

p_{A} = 2 p_{B}

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2 p_{A} = 3 p_{B}

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p_{A} = 3 p_{B}

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3 p_{A} = 2 p_{B}

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Solution

The correct option is B $2 p_{A} = 3 p_{B}$
Given, $Z_{A} = 3 Z_{B}$ (i)
Compressibility factor (Z) = $\frac{p V}{n R T} (f o r r e a l g a s e s)$
On substituting in equation (i), we get
$\frac{p_{A} V_{A}}{n_{A} R T_{A}} = \frac{3 p_{B} V_{B}}{n_{B} R T_{B}}$ (ii)
Also, it is given that
$V_{A} = 2 V_{B}, n_{A} = n_{B} a n d T_{A} = T_{B}$
$∴$ Eq. (ii) becomes
$\frac{p_{A} \times 2 V_{B}}{n_{A} R T_{B}} = \frac{3 p_{B} V_{B}}{n_{B} R T_{B}}$
$\Rightarrow 2 P_{A} = 3 P_{B}$

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