When the gas temperature changed from 13 degrees to 52, its pressure increased by

When the gas temperature changed from 13 degrees to 52, its pressure increased by 117 mm Hg. Find the initial gas pressure if its volume has not changed?

Given:

t1 = 13 degrees Celsius = 286 degrees Kelvin;

t2 = 52 degrees Celsius = 325 degrees Kelvin;

P2 = P1 + 117 mm Hg column = P1 + 15,600 Pa.

Find P1.

According to Boyle-Mariotte’s law:

P1 / t1 = P2 / t2, P1 / t1 = (P1 + 15600) / t2, hence:

P1 = 15600 * t1 / (t2 – t1) = 15600 * 286 / (325 – 286) = 4461600/39 = 114 400 Pa or 858 mm Hg column.

Answer: the initial gas pressure was 114,400 Pa (858 mm Hg).