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ICSE Class 9 Chemistry Question 28 of 29

Study of Gas Laws — Question 11

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11
Question

Question 3.5

A gas X is collected over water at 17°C and 750 mm. pressure. If the volume of the gas collected is 50 cc., calculate the volume of the dry gas at s.t.p. [at 17°C the vapour pressure is 14 mm.]

Answer
Initial conditionsFinal conditions [S.t.p.]
P1 = Initial pressure of the gas = 750 mm - 14 mm = 736 mmP2 = Final pressure of the gas = 760 mm
V1 = Initial volume of the gas = 50 cc.V2 = Final volume of the gas = ?
T1 = Initial temperature of the gas = 17°C = 17 + 273 = 290 KT2 = Final temperature of the gas = 273 K

By Gas Law:

P1×V1T1=P2×V2T2\dfrac{\text{P}_1\times\text{V}_1}{\text{T}_1} = \dfrac{\text{P}_2\times\text{V}_2}{\text{T}_2}

Substituting the values :

736×50290=760×V2273V2=736×50×273290×760V2=1,00,46,4002,20,400V2=45.58 cc.\dfrac{736\times 50}{290} = \dfrac{760\times\text{\text{V}}_2}{273} \\[1em] \text{V}_2 =\dfrac{736\times 50 \times 273}{290\times 760} \\[1em] \text{V}_2 =\dfrac{1,00,46,400}{2,20,400} \\[1em] \text{V}_2 = 45.58 \text{ cc.}

Therefore, final volume of the gas = 45.58 cc