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

1711.11L

Step-by-step 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 =
`(mass)/(molar mass)`

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

Number of moels of methane =
`(1000)/(16)` = 62.5mole

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

V =
`(nRT)/(P)`

V =
`(62.5 x 0.082 x 308)/(0.9)` = 1711.11L