Answer to Question #177503 in General Chemistry for Adejuwon benjamin

Question

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

Answer 1

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.