A Sample of Nitrogen Gas: Temperature and Volume Relationship

A sample of nitrogen occupies 3.50 liters under a pressure of 900. torr at 25.0 oC. At what temperature will it occupy 7.0 liters at the same pressure?

C. 323 °C

To solve this problem, we can use the combined gas law equation, which relates the initial and final volumes, pressures, and temperatures of a gas sample. The equation is:

(P1 * V1) / (T1) = (P2 * V2) / (T2)

Where:

P1 = Initial pressure

V1 = Initial volume

T1 = Initial temperature

P2 = Final pressure

V2 = Final volume

T2 = Final temperature

Given:

P1 = 900 torr

V1 = 3.50 liters

T1 = 25.0 °C

P2 = 900 torr

V2 = 7.0 liters

Converting the temperatures to Kelvin scale:

T1 = 25.0 °C + 273.15 = 298.15 K

Rearranging the equation to solve for T2:

T2 = (P2 * V2 * T1) / (P1 * V1)

Substituting the given values:

T2 = (900 torr * 7.0 liters * 298.15 K) / (900 torr * 3.50 liters)

T2 = 2 * 298.15 K

T2 = 596.3 K

Converting the temperature back to Celsius:

T2 = 596.3 K - 273.15 = 323.15 °C

Therefore, the temperature at which the nitrogen will occupy 7.0 liters at the same pressure is approximately 323 °C.

The temperature required for the nitrogen to occupy 7.0 liters at the same pressure is approximately 323 °C.