Two moles of an ideal gas have a volume of 3.43X10-3m3. the initial temperature of the gas is 78.0C. If the pressure is held constant while it is heated to a final temetatue of 275C, what would be the final volume?
To find the final volume of the gas, we can use the combined gas law equation:
P1 * V1 / T1 = P2 * V2 / T2
where P1 and P2 are the initial and final pressures, V1 and V2 are the initial and final volumes, and T1 and T2 are the initial and final temperatures in Kelvin.
First, let's convert the initial and final temperatures from Celsius to Kelvin:
T1 = 78.0°C + 273.15 = 351.15 K
T2 = 275°C + 273.15 = 548.15 K
Since the pressure is held constant, we have P1 = P2. Let's substitute the given values into the equation:
P1 * V1 / T1 = P2 * V2 / T2
Since P1 = P2:
V1 / T1 = V2 / T2
Now, we can rearrange the equation to solve for V2:
V2 = (V1 * T2) / T1
Substituting the known values into the equation:
V2 = (3.43 × 10^(-3) m³) * (548.15 K) / (351.15 K)
Calculating the expression on the right side of the equation:
V2 = 5.353 × 10^(-3) m³
Therefore, the final volume of the gas would be approximately 5.353 × 10^(-3) m³.