Question

Calculate to what temperature 75.0 grams of carbon tetrachloride gas, CCl4 would need to be heated to have a volume of 2.00 liters at 250 °C.

(Ideal Gas Law Problem)

Answer 1

The CCl4 gas would need to be heated to -178.7 °C to have a volume of 2.00 liters at 250 °C.

Explanation:

First, we need to calculate the number of moles of CCl4:

`\sf:\implies n = (m)/(M)`

`\sf:\implies n = (75.0\: g)/(154.0\: g/mol)`

`\sf:\implies n = 0.487\: moles`

Next, we can use the ideal gas law to solve for the temperature:

`\sf\qquad\dashrightarrow PV = nRT`

where:

• P is the pressure
• V is the volume
• n is the number of moles
• R is the gas constant (0.08206 L·atm/mol·K)
• T is the temperature in Kelvin

We need to convert the given temperature of 250 °C to Kelvin:

`\sf:\implies T = 250 ^(\circ)C + 273.15`

`\sf:\implies T = 523.15\: K`

Now we can plug in the values and solve for T:

`\sf:\implies (1\: atm)(2.00\: L) = (0.487\: mol)(0.08206\: L\cdot atm/mol\cdot K)T`

`\sf:\implies T = ((1\: atm)(2.00\: L))/((0.487\: mol)(0.08206\: L\cdot atm/mol\cdot K))`

`\sf:\implies T = 94.5\: K`

Finally, we need to convert the temperature back to Celsius:

`\sf:\implies T = 94.5\: K - 273.15`

`\sf:\implies \boxed{\bold{\:\:T = -178.7 ^(\circ)C\:\:}}\:\:\:\green{\checkmark}`

Therefore, the CCl4 gas would need to be heated to -178.7 °C to have a volume of 2.00 liters at 250 °C.

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