Question

At STP the density of chlorine is 3.22 kg/m3 .what is the weight of this gas if it is contained in a flask of 100cm3 at 28°C and 100 kPa?

Answer 1

Let's write Mendeleyev-Clapeyron's law at STP:

$$P _ {0} V _ {0} = \frac {m}{M} R T _ {0}$$

So,

$$M = \frac {m}{V _ {0}} \frac {1}{P _ {0}} R T _ {0}$$

It's easy to notice, that $\frac{m}{V_0} = \rho$ , where $\rho$ is density.

$$M = \frac {1}{P _ {0}} \rho R T _ {0}$$

Let's write Mendeleyev-Clapeyron's law for gas in flask:

$$P V = \frac {m}{M} R T$$

So,

$$m = \frac {P V M}{R T}$$

Substituting $M$ :

$$m = \frac {P V \rho R T _ {0}}{P _ {0} R T} = \rho V \frac {P T _ {0}}{P _ {0} T}$$

So,

$$m = 3.22 * 100 * 10 ^ {- 6} \frac {100 * 10 ^ {3} * 273}{100 * 10 ^ {3} * 301} = 2.92 * 10 ^ {- 4} (kg)$$