A coal-fired power station is used to generate electricity - VCE - SSCE Chemistry - Question 2 - 2022 - Paper 1

To determine the pressure of the CO₂ in the tank, we will use the ideal gas law given by the equation:

$PV = nRT$

where:

• ( P ) = pressure in pascals
• ( V ) = volume in cubic meters
• ( n ) = number of moles
• ( R ) = ideal gas constant (8.314 J/(mol·K))
• ( T ) = temperature in Kelvin

1. Convert the temperature to Kelvin: ( T = 28.0 °C + 273.15 = 301.15 , K )

2. Convert the volume from liters to cubic meters: ( V = 20000.0 , L \times 0.001 = 20.0 , m^3 )

3. Calculate the pressure: Re-arranging the ideal gas law gives us: ( P = \frac{nRT}{V} )

   Substituting in the values:

   • ( n = 5.17 \times 10^{4} , mol )
   • ( R = 8.314 , J/(mol·K) ) (which is equivalent to ( 8.314 , Pa·m^3/(mol·K) ))
   • ( T = 301.15 , K )

   [ P = \frac{(5.17 \times 10^{4}) \times (8.314) \times (301.15)}{20.0} ]

   [ P \approx \frac{1280209.4587}{20.0} \approx 64010.47 , Pa ] Since 1 kPa = 1000 Pa: [ P \approx \frac{64010.47}{1000} \approx 64.01 , kPa ]

Thus, the pressure in the tank is approximately 64.01 kPa.