Question

The planet Jupiter is composed mostly of hydrogen gas.To what temperature, in ºc, must a 20.2 g sample of hydrogen gas be heated to, at 140 kPa, tooccupy a volume of 224 L?

Answer 1

We are asked to find the temperature of hydrogen gas (H2) given certain pressure and temperature conditions. Since the pressure to which the gas will be subjected is low we can apply the ideal gas law which is represented by the following equation:

`PV=nRT`

Where,

P= Pressure = 140kPa = 1.38169 atm

V= Volumen = 224 L

R= Ideal gas constant = 0.08206 (atm L)/(mol K)

n= Number of moles

T= Temperature in K

Now we are going to find the number of moles of the gas, n. We will use the molar mass of the hydrogen gas (2.01594g/mol). So, we have:

`n=\text{ }\frac{\text{Mass}}{Molar\text{ mass}}=\frac{20.2\text{ g}}{2.01594\text{ g/mol}}=10.02\text{ mol}`

Now, we will clear the temperature T from the first equation:

`T=(PV)/(nR)`

We replace the known values:

`\begin{gathered} T=(1.38169atm*224L)/(10.02mol*0.08206(atm.L)/(mol.K)) \\ T=376.40K \end{gathered}`

So, the temperature of hydrogen gas will be 376.40K