The temperature of nitrogen is unknown when the gas occupies 100.0 mL at 99.10 kPa. If the gas is known to occupy 74.2 mL at 133.7 kPa and 305 K, determine the unknown temperature.

The unknown temperature is 304.7K

Explanation:

V1 = 100mL = 100*10^-3L

P1 = 99.10kPa = 99.10*10³Pa

V2 = 74.2mL = 74.2*10^-3L

P2 = 133.7kPa = 133.7*10³Pa

T2 = 305K

T1 = ?

From combined gas equation,

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

Solving for T1,

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

T1 = (99.10*10³ * 100*10^-3 * 305) / (133.7*10³ * 74.2*10^-3)

T1 = 3022550 / 9920.54

T1 = 304.67K

T1 = 304.7K