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 gas in the tank, we can use the ideal gas law, given by the formula:

$PV = nRT$

Where:

• $P$ is the pressure in pascals (Pa)
• $V$ is the volume in liters (L)
• $n$ is the number of moles of gas
• $R$ is the ideal gas constant, approximately 8.314 rac{J}{K imes mol}
• $T$ is the temperature in Kelvin (K)

First, we need to convert the given temperature from Celsius to Kelvin:

$T = 28.0 °C + 273.15 = 301.15 K$

Inserting the values into the equation, we convert the volume from liters to cubic meters for proper SI units:

$V = 20000.0 L = 20000.0 imes 10^{-3} m^3 = 20 m^3$

Now substituting the known values into the ideal gas law:

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

Substituting:

• $n = 5.17 \times 10^{4} mol$
• $R = 8.314 \frac{J}{K \times mol} = 8.314 \frac{Pa \cdot m^3}{K \cdot mol}$
• $T = 301.15 K$
• $V = 20 m^3$

Calculation: $P = \frac{(5.17 \times 10^{4} mol)(8.314 \frac{Pa \cdot m^3}{K \cdot mol})(301.15 K)}{20 m^3}$

$P = \frac{1295731.63}{20} = 64786.58 Pa$

Since 1 kPa = 1000 Pa, converting this to kilopascals gives: $P = \frac{64786.58 Pa}{1000} = 64.79 kPa$

Thus, the pressure in the tank is approximately 64.79 kPa.