Calculate the final Celsius temperature of sulfur dioxide if 0.500 L of the gas at 35°C and 650 mmHg is heated until the pressure reaches 742 mmHg. Assume the volume remains 0.500 L.
(P1/T1) = (P2/T2)
Remember T is in kelvin.
To calculate the final Celsius temperature of sulfur dioxide gas, we can use the ideal gas law equation, which is given as:
PV = nRT,
where:
P = pressure of the gas (in atm)
V = volume of the gas (in liters)
n = number of moles of gas
R = ideal gas constant (0.0821 L·atm/mol·K)
T = absolute temperature of the gas (in Kelvin)
To solve for the final temperature (T2), we need to convert the given pressures (650 mmHg and 742 mmHg) to atm and convert the given temperature (35°C) to Kelvin.
Step 1: Convert the given pressures from mmHg to atm:
650 mmHg * (1 atm / 760 mmHg) = 0.855 atm
742 mmHg * (1 atm / 760 mmHg) = 0.976 atm
Step 2: Convert the given temperature from Celsius to Kelvin:
35°C + 273.15 = 308.15 K
Step 3: Plug the values into the ideal gas law equation:
P1 * V1 / T1 = P2 * V2 / T2,
where:
P1 = initial pressure (0.855 atm)
V1 = initial volume (0.500 L)
T1 = initial temperature (308.15 K)
P2 = final pressure (0.976 atm)
V2 = final volume (0.500 L)
T2 = final temperature (to be calculated)
0.855 * 0.500 / 308.15 = 0.976 * 0.500 / T2.
Step 4: Solve for T2:
0.442275 = 0.488 / T2
Cross multiply and solve for T2:
T2 * 0.442275 = 0.488
T2 = 0.488 / 0.442275
T2 ≈ 1.104 K
Step 5: Convert the final temperature from Kelvin to Celsius:
T2 - 273.15 = 1.104 - 273.15 ≈ -271.05°C
Therefore, the final Celsius temperature of sulfur dioxide gas is approximately -271.05°C.