A rigid tank contains $35 k g$ of nitrogen at $6 a t m$ . Sufficient quantity of oxygen is supplied to increase the pressure to $9 a t m$ , while the temperature remains constant. Amount of oxygen supplied to the tank is :

5 k g

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10 k g

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20 k g

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40 k g

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Solution

The correct option is C $20 k g$
The amount of oxygen added to increasew the pressure from $6$ atm to $9$ atm will be $20$ kg.

From the gas law we know that,

$P V = n R T$

Since $V, R$ and $T$ are constant here,

$⟹ P α n$

Since pressure is increased by $1.5$ times, hence number of moles should also increase by $1.5$ times.

So, oxygen added should be equal to half the nymber of moles of nitrogen.

Number of moles of nitrogen in $35$ kg $= \frac{35000}{14} = 2500$ moles

Hence, number of moles of oxygen $= \frac{2500}{2} = 1250$ moles

One mole of oxygen weight $= 16 g$

$⟹ 1250$ moles of oxygen weight $= 1250 \times 16 = 20000 g = 20 k g$

Hence the amount of oxygen added to increase the pressure from $6$ atm to $9$ atm will be $20 k g$ .

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A rigid tank contains 35 kg of nitrogen at 6 atm. Sufficient quantity of oxygen is supplied to increase the pressure to 9 atm, while the temperature remains constant. Amount of oxygen supplied to the tank is :

A rigid tank contains $35 k g$ of nitrogen at $6 a t m$ . Sufficient quantity of oxygen is supplied to increase the pressure to $9 a t m$ , while the temperature remains constant. Amount of oxygen supplied to the tank is :