Answer :
Therefore, the volume of the gas sample when heated to a temperature of 85°C at constant pressure will be approximately 12.03 liters.
To find the final volume of the gas sample when heated at constant pressure, we can use the combined gas law:
P1 * V1 / T1 = P2 * V2 / T2
Where:
P1 = initial pressure
V1 = initial volume
T1 = initial temperature (in Kelvin)
P2 = final pressure
V2 = final volume (unknown)
T2 = final temperature (in Kelvin)
First, let's convert the initial and final temperatures to Kelvin:
T1 = 44°C + 273.15 = 317.15 K
T2 = 85°C + 273.15 = 358.15 K
Now, we can plug in the given values into the equation:
(754 mm Hg) * (13.7 L) / (317.15 K) = P2 * V2 / (358.15 K)
Rearranging the equation to solve for V2:
V2 = (P2 * V1 * T2) / (P1 * T1)
Plugging in the known values:
V2 = (754 mm Hg * 13.7 L * 358.15 K) / (317.15 K * 1 atm)
Converting mm Hg to atm:
1 atm = 760 mm Hg
V2 = (754 mm Hg * 13.7 L * 358.15 K) / (317.15 K * 760 mm Hg)
Calculating V2:
V2 ≈ 12.03 L
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