# Hydrogen at a temperature of 15 C and a pressure of 1.33 multiplied by 10 to the fifth

Hydrogen at a temperature of 15 C and a pressure of 1.33 multiplied by 10 to the fifth power of Pa takes 2 liters. The gas was compressed to 12.5 liters and the temperature was raised to 30 degrees C. What was the gas pressure?

M = 0.002 kg / mol.

T1 = 288 ° K.

V1 = 2 l = 0.002 m3.

P1 = 1.33 * 10 ^ 5 Pa.

V2 = 1.5 l = 0.0015 m3.

T2 = 303 ° C.

R = 8.31 m2 * kg / s2 * ° K * mol.

P2 -?

Let us write the Mendeleev-Cliperon equation for gas before and after compression: P1 * V1 = m * R * T1 / M, P2 * V2 = m * R * T2 / M.

P2 = m * R * T2 / V2 * M.

Since the mass of the gas did not change during expansion, we express it from the first equation and substitute it into the second.

m = P1 * V1 * M / R * T1.

P2 = P1 * V1 * M * R * T2 / V2 * M * R * T1 = P1 * V1 * T2 / V2 * T1.

P2 = 1.33 * 10 ^ 5 Pa * 0.002 m3 * 303 ° K / 0.0015 m3 * 288 ° K = 1.86 * 10 ^ 5 Pa.

Answer: the hydrogen pressure after compression will become P2 = 1.86 * 10 ^ 5 Pa.

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