Question #177503

30cm3 of hydrogen was collected over water at 27°c and 750mmhg, if the vapor pressure of the water at the temperature of the experiment was 100mmhg. Calculate the volume of the gas of 760mmhg and 27°c

330cm

1
2021-04-02T05:11:56-0400

Q177503

30cm3 of hydrogen was collected over water at 27°c and 750mm Hg. If the vapor pressure of the water at the temperature of the experiment was 100mm Hg. Calculate the volume of the gas of 760mmhg and 27°c.

Solution :

We have to find the volume of the dry hydrogen gas ( without any water ) at 760 mm Hg and 27 oC.

Let us first find the partial pressure of hydrogen gas at 27 oC.

Total pressure = Partial pressure of hydrogen gas + vapor pressure of water vapor.

"750\\space mm\\space Hg = Partial\\space pressure\\space of\\space hydrogen\\space gas + 100\\space mm\\space Hg"

"Partial\\space pressure\\space of\\space hydrogen\\space gas = 750\\space mm\\space Hg - 100\\space mm\\space Hg"

"Partial\\space pressure\\space of\\space hydrogen\\space gas = 650\\space mm\\space Hg"

Hence the partial pressure of hydrogen gas in the collected moist hydrogen gas will be 650 mm Hg.

Step 2 :

We have to find out the volume occupied by pure hydrogen gas at 760 mm Hg and 270C.

The temperature is the same. Only the pressure is changed.

The pressure of hydrogen gas, P1 = 650 mm Hg,

the initial volume of hydrogen gas, V1 = 30 cm3.

New pressure of hydrogen gas, P2 = 760 mm Hg.

new volume of hydrogen gas, V2 =?

We can use Boyle's law, P1 V1 = P2 V2, and find the new volume occupied by hydrogen gas.

"P_2 V_2 = P_1 V_1"

"760 \\space mm\\space Hg * V_2 = 650\\space mm\\space Hg * 30 cm^3 ."

divide both the side by 760 mm Hg, we have

"\\frac{760 \\space mm\\space Hg * V_2 }{760 \\space mm\\space Hg } = \\frac{650\\space mm\\space Hg * 30 cm^3}{760 \\space mm\\space Hg}"

"V_2 = \\frac{650\\space mm\\space Hg * 30 cm^3}{760 \\space mm\\space Hg} = \\frac{19500 cm^3 }{760 }"

"V_2 = 25.66\\space cm^3."

### Hence the volume of hydrogen gas at 760mm Hg and 27°C will be 26 cm3.

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