Question

A 3.6 mole sample of methane gas is kept in a 1.50 liter container at a temperature of 100°C. What is the pressure of the gas?

Answer 1

I get `7442.7 \ "kPa"`.

Explanation:

We use the ideal gas law, which states that,

`PV=nRT`

• `P` is the pressure

• `V` is the volume in liters (for this case)

• `n` is the number of moles of the substance

• `R` is the ideal gas constant, which varies

• `T` is the temperature in Kelvin

Since we need to find pressure, we can rearrange the equation into:

`P=(nRT)/V`

Now, we need to convert the temperature into Kelvin. We know that `"K"=""^@"C"+273.15`, and so `100^@"C"=100+273.15=373 \ "K"`.

Since our temperature is in `"K"` and volume in liters, let's use `R=8.314 \ "L" \ "kPa" \ "K"^-1 \ "mol"^-1`. Taken from: https://en.wikipedia.org/wiki/Gas_constant

And so, we find that the pressure is:

`P=(3.6 \ "mol"*8.314 \ "L" \ "kPa" \ "K"^-1 \ "mol"^-1*373 \ "K")/(1.5 \ "L")`

`=(11164.0392color(red)cancelcolor(black)"mol"color(red)cancelcolor(black)"L" \ "kPa"color(red)cancelcolor(black)"K"^-1color(red)cancelcolor(black)"mol"^-1color(red)cancelcolor(black)"K")/(1.5color(red)cancelcolor(black)"L")`

`=7442.6928 \ "kPa"`

`~~7442.7 \ "kPa"`