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Hot copper tu...

Question

Hot copper turnings can be used as an oxygen getter for inert gas supplies by slowly passing the gas over the turnings at $600 K$ .
$2 C u (s) + 1 / 2 O_{2} (g) ⇌ C u_{2} O (s); K_{p} = 7.5 \times 10^{10} {a t m}^{- 1 / 2}$
The number of molecules of $O_{2}$ are left in one litre of a gas supply after equilibrium has been reached is $X$ . $10 X$ is__________.

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Solution

$K_{p} = P_{O_{2}}^{- 0.5}$
$P_{O_{2}} = (K_{P})^{- 2} = (7.5 \times 10^{10})^{- 2} = 1.77 \times 10^{- 22}$ atm

Volume is 1 L and temperature is 600 K. The number of moles
$n = \frac{P V}{R T} = \frac{1.77 \times 10^{- 22} \times 1}{0.08206 \times 600} = 3.61 \times 10^{- 24}$

The number of oxygen molecules is obtained by multiplying number of moles with Avogadro's number.

Number of oxygen molecules $= 3.61 \times 10^{- 24} \times 6.023 \times 10^{23} = 2.2$

But it is equal to X
$X = 2.2$
$10 X = 22$

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