To what Celsius temperature must 1.50 atm of hydrogen gas at 16.3°C be changed so the pressure will be 2.18 atm? Assume the volume and the amount of gas are held constant.

Answer 1

Hello Jared,

Recall the Ideal Gas Law, PV = nRT, where P is pressure, V is volume, n is the amount of gas (in moles), T is temperature (in degrees Kelvin), and R is a constant. It follows from the Ideal Gas Law that if n and V are constant, then pressure and temperature are directly proportional. This can be expressed as

P/T = constant, or equivalently,

(Eq.1) P_f/T_f = P_i/T_i

where i ="initial" and f = "final". As in the Ideal Gas Law, T must be expressed in Kelvin in order to use this equation. If T_i = 16.3°C, then, in the Kelvin scale, T_i = 16.3 + 273.15 = 289.45K.

Substituting the given information into Eq.1 and solving for T_f, we have

2.18atm/T_f = (1.50atm)/(289.45K)

T_f ≅ 420.67K.

Subtracting 273.15 to convert back to Celsius gives the final result

T_f = 147.52°C

Hope that helps!

William