Answer:
992.302 K
Explanation:
V(rms) = 750 m/s
V(rms) = √(3RT / M)
V = velocity of the gas
R = ideal gas constant = 8.314 J/mol.K
T = temperature of the gas
M = molar mass of the gas
Molar mass of CO₂ = [12 + (16*2)] = 12+32 = 44g/mol
Molar mass = 0.044kg/mol
From
½ M*V² = 3 / 2 RT
MV² = 3RT
K = constant
V² = 3RT / M
V = √(3RT / M)
So, from V = √(3RT / M)
V² = 3RT / M
V² * M = 3RT
T = (V² * M) / 3R
T = (750² * 0.044) / 3 * 8.314
T = 24750000 / 24.942
T = 992.302K
The temperature of the gas is 992.302K
Note : molar mass of the gas was converted from g/mol to kg/mol so the value can change depending on whichever one you use.
The temperature of CO2 gas if the average speed of the molecules is 750 m/s is;
T = 9.92 × 10² K
Formula for root mean square speed is;
V_rms = √(3RT/M)
Where;
V is speed of the gas
R is ideal gas constant = 8.314 J/mol.K
T is temperature of the gas
M is molar mass of the gas
Now, from tables, Molar mass of CO₂ = 0.044kg/mol
We are given; V_rms = 750 m/s
Thus;
750 = √(3 × 8.314 × T/0.044)
Square both sides to eradicate the square root;
750² = 3 × 8.314 × T/0.044
Making T the subject gives;
T = (750² × 0.044)/(3 × 8.314)
T = 9.92 × 10² K
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