Answer:
236.9g
Explanation:
Given parameters:
Volume of gas = 81.3L
Pressure of gas = 204kPa
temperature of gas = 95°C
Unknown:
Mass of carbondioxide gas = ?
Solution:
To solve this problem, the ideal gas law will be well suited. The ideal gas law is a fusion of Boyle's law, Charles's law and Avogadro's law.
Mathematically, it is expressed as;
PV = nRT
the unknown here is n which is the number of moles;
P is the pressure, V is the volume, R is the gas constant and T is the temperature.
convert pressure into atm
101.325KPa = 1atm
204 kPa = [tex]\frac{204}{101.325}[/tex] = 2atm
Convert temperature to Kelvin; 95 + 273 = 368K
2 x 81.3 = n x 0.082 x 368
n = [tex]\frac{2 x 81.3}{0.082 x 368}[/tex] = 5.38moles
Since the unknown is mass;
Mass = number of moles x molar mass
Molar mass of carbon dioxide = 12 + 2(16) = 44g/mol
Mass = 5.38 x 44 = 236.9g
The mass of carbon dioxide gas that occupies a volume of 81.3L at 204 KPa and a temperature of 95.0°C is 238.5g.
The mass of the carbon dioxide can be calculated by multiplying the number of moles of CO2 by its molar mass.
However, the number of moles of CO2 must be calculated first by using the ideal gas law equation:
PV = nRT
Where;
2.013 × 81.3 = n × 0.0821 × 368
163.66 = 30.21n
n = 5.42mol
mass = 5.42 × 44
mass = 238.5g
Therefore, the mass of carbon dioxide gas that occupies a volume of 81.3L at 204 KPa and a temperature of 95.0°C is 238.5g.
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