# A sample of O2 under 2.00 atm occupies 500 ml at 25.0˚C. What temperature will be needed to produce a pressure of 4.00 atm?

May 15, 2014

This problem assumes that the volume is being held constant at 500 mL. Therefore, we would use the Gay-Lussac (Pressure-Temperature) equation.

Pressure and Temperature have a direct relationship as determined by Gay-Lussac Law

$\frac{P}{T} = \frac{P}{T}$

Pressure and temperature will both increase or decrease simultaneously as long as the volume is held constant.

Therefore if temperature were to increase the pressure would likewise increase. Increased pressure would increase the energy of the molecules and the number of collisions would therefore increase causing an increase in temperature. More collisions within the system, leads to more collisions with the surface of the container and therefore more temperature within the system.

Take a sample of ${O}_{2}$ gas at 2.00 atm and 25 C and increase the pressure to 4.00 atm, what will the new temperature be.

First we must convert the Celsius temp to Kelvin, 25 C + 273 = 298 K

$\frac{2.00 a t m}{298 K} = \frac{4.00 a t m}{x K}$

Rearrange the equation algebraically

$x K = \frac{4.00 a t m K}{298 K} / \left(2.00 a t m\right)$

T = 596 K

$596 - 273 = 323 C$