Name: Kinetic Theory and Temperature
Uploaded: 2019-07-19
Duration: 5 min 52 s
Description: We know that kinetic energy is the energy possessed due to the motion of an object. How does kinetic energy work in gases, and how does the temperature affec...

Question

A large flask fitted with a stop-cock is evacuated and weighed; its mass is found to be $134.567 g$ . It is then filled to a pressure of $735 mm$ at $31^{o} C$ with a gas of unknown molecular mass and then reweighed; its mass is $137.456 g$ .

The flask is then filled with water and weighed again; its mass is now $1067.9 g$ . Assuming that the gas is ideal, calculate the molar mass of the gas.

Accepted Answer

The flask is filled with water weighed $= 1067.9 g$

The evacuated flask fitted with stop-cock weighed $= 134.567 g$

Mass of water filling the flask $= (1067.9 - 134.567) g = 933.33 g$

$∴$ Volume of flask $=$ Volume of water filling the flask $= 933.33 {cm}^{3}$ (density of $H_{2} O = 1 {gcm}^{- 3}$ )

Now, $P = 735 mm, T = 31 + 273 K = 304 K, V = 933.33 {cm}^{3}$ , Molar mass $= ?$

Applying $PV = nRT,$ i.e., $(\frac{735}{760} atm) (\frac{933.33}{1000} L) = n \times 0.0821 L atm K^{- 1} {mol}^{- 1} \times 304 K$

This gives, $n = 0.036 mol$

The unknown molecular mass of the gas reweighed $= 137.456 g$

The evacuated flask fitted with stop-cock weighed $= 134.567 g$

Mass of $0.036 mol$ of the gas $= (137.456 - 134.567) g = 2.889 g$

$∴$ Molar mass of the gas $= \frac{Mass}{no . of moles} = \frac{w}{n} = \frac{2.889}{0.036} = 80.25 g / mol$

Important Questions on States of Matter : Gases and Liquids

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