Question

A sample of nitrogen occupies 5.50 liters under a pressure of 900 torr at 25oC. At what temperature will it occupy 10.0 liters at the same pressure?

Answer 1

Answer:

At 268.82°C volume occupied by nitrogen is 10 liters at pressure of 900 torr.

Explanation:

Given:

Volume of a sample of nitrogen = 5.50 liters

Pressure = 900 torr

Temperature = 25°C

To find the temperature at which the nitrogen will occupy 10 liters volume at same pressure.

Solution:

Since the pressure is kept constant, so we can apply the temperature-volume law also called the Charles Law.

Charles Law states that the volume of a gas held at constant pressure is directly proportional to the temperature of the gas in Kelvin.

Thus, we have :

$V$ ∝ $T$

$\frac{V}{T}=k$

where $k$ is a constant.

For two samples of gases, the law can be given as:

$\frac{V_1}{T_1}=\frac{V_2}{T_2}$

From the data given:

$V_1=5.5\ l$

$T_1=25\ \°C =(273+25)K= 298 K$

$V_2=10\ l$

We need to find $T_2$.

Plugging in values in the formula.

$\frac{5.5}{298}=\frac{10}{T_2}$

Multiplying both sides by $T_2$.

$T_2\times\frac{5.5}{298}=\frac{10}{T_2}\times T_2$

$\frac{5.5}{298}T_2={10}$

Multiplying both sides by $\frac{298}{5.5}$

$\frac{298}{5.5}\times\frac{5.5}{298}T_2=\frac{10\times 298}{5.5}$

$T_2=541.82\ K$

$T_2=541.82\ K-273\ K = 268.82\°C$

Thus, at 268.82°C volume occupied by nitrogen is 10 liters at pressure of 900 torr.