Question

If the pressure of 50.0 mL of oxygen gas at 100°C increases from 735 mm Hg to 925 mm Hg, what is the final volume? Assume the temperature remains constant.

Answer 1

`"volume" = 0.03976L`

Explanation:

Recall the gas law

`PV = nRT`

`P = (nRT)/V`

Our question
If the pressure of 50.0 mL of oxygen gas at 100°C increases from 735 mm Hg to 925 mm Hg, what is the final volume? Assume the temperature remains constant.
This means

`735mmHg = "{n * 0.0821L * (100C + 273K )}"/ ("50.0mL "/"1000ml" )`

mmHg must be converted in `atm` , `"celsius to kelvin"` and `"ml to Litres"`

=1 atm = 760mmHg

`"735mmHg" /"760mmHg" = 0.96711atm`

0.9671053242406501atm = n * 0.0821L * 373K/0.05L

Solve the equation

`0.9671053242406501atm = "30.6233n"/"0.05L"`

Multiply both sides with 0.05L

`\frac{30.6233n}{0.05L}*0.05=0.96711atm *0.05L`

`30.6233n=0.0483555`

`n = 30.6233/0.048355`

n = 0.00158moles

So lets now calculate volume when we know n.
n is constant in both the equation.

`"925mmHg"/"760mmHg" = 1.2171052631578947368421052631579atm`

`1.21711atm = "(0.00158 * 0.0821L * 373K)"/V`

`1.21711atm = 0.048384814/V`

`V = 0.048384814/"1.21711atm"`

`V = 0.03976L`

`"volume" = 0.03976L`