Question

A 0.275 m^3 tank contains hydrogen (H2) at a temperature of 10° C and a gauge pressure of 3.55 x 10^4 Pa. (a) What is the absolute temperature? (b) What is the absolute pressure? (c) How many moles of H2 are there in the tank? (d) What is the root mean square speed of the H2 molecules?

Answer 1

a) 283 K

b) 136825 Pa

c) 15.992

d) 1878.6 m/s

Step-by-step explanation:

a)

T = absolute temperature = 10 °C = 10 + 273 = 283 K

b)

`P_(atm)` = Atmospheric pressure = 101325 Pa

`P_(gauge)` = gauge pressure = 35500 Pa

Absolute pressure is given as

`P_(abs) = P_(atm) + P_(gauge)`

`P_(abs) = 101325 + 35500`

`P_(abs) = 136825` Pa

c)

`n` = number of moles of Hydrogen

`V` = Volume of hydrogen = 0.275 m³

Using the equation

`P_(abs) V = n R T`

`(136825) (0.275) = n (8.314) (283)`

`n` = 15.992

d)

`M` = Molar mass of hydrogen = 2 g mol⁻¹ = 0.002 kg mol⁻¹

`V` = root mean square speed

Root mean square speed is given as

`V = \sqrt{(3RT)/(M) }`

`V = \sqrt{(3(8.314)(283))/(0.002) }`

`V = 1878.6` m/s