Question

3. Methane (CH4) behaves as an ideal gas under standard temperature and pressure conditions. What volume is occupied by 1 kg of methane at a temperature of 35 °C and a pressure of 0.9 atm?

Answer 1

Answer:

1711.11L

Explanation:

Given parameters:

Mass of methane = 1kg = 1000

Temperature of gas = 35°C

Pressure of the gas = 0.9atm

Converting to the temperature to kelvin, we have:

               35+ 273 = 308k

Solution

From the given parameters, we can solve this problem using the ideal gas equation which is combination of the gas laws. It is expressed below:

                                         PV = nRT              .......................(i)

Where P is the pressure of the gas

             V is the volume of the gas

             n is the number of moles

             R is the gas constant

             T is the temperature

Now, from the above parameters, we have two unknowns which are n and V.

To find the number of moles n, we use the expression below:

         number of moles = $\frac{mass}{molar mass}$

        molar mass of methane = 12 + (4x1) = 16g/mol

       Number of moels of methane =  $\frac{1000}{16}$ = 62.5mole

Now that we know the number of moles, we can make the unknown Volume the subject of the formula:

                     V = $\frac{nRT}{P}$

                     V =  $\frac{62.5 x 0.082 x 308}{0.9}$ = 1711.11L