A sample of gas is in a 50.0mL container at a pressure of 86 kPa and a temperature of 25°C. The entire sample is heated to a temperature of 35°C and transferred to a new container whose volume is 65.0mL. The pressure of the gas in the second container is:
64 kPa
115.6 kPa
101.3 kPa
92.5 kPa
none of these
To find the pressure of the gas in the second container, we can use the ideal gas law equation, which states:
PV = nRT
Where:
P = pressure of the gas
V = volume of the gas
n = number of moles of gas
R = ideal gas constant
T = temperature of the gas in Kelvin
First, let's convert the temperatures from Celsius to Kelvin by adding 273.15:
Initial temperature (T1) = 25°C + 273.15 = 298.15 K
Final temperature (T2) = 35°C + 273.15 = 308.15 K
Next, let's convert the volumes from mL to L by dividing by 1000:
Initial volume (V1) = 50.0 mL / 1000 = 0.050 L
Final volume (V2) = 65.0 mL / 1000 = 0.065 L
Now, let's rearrange the ideal gas law equation to solve for the final pressure (P2):
P2 = (n * R * T2) / V2
Since the number of moles and the ideal gas constant are constant, we can simplify the equation:
P2 = P1 * (V1 / V2) * (T2 / T1)
Substituting the values into the equation:
P2 = 86 kPa * (0.050 L / 0.065 L) * (308.15 K / 298.15 K)
P2 = 86 kPa * (0.7692) * (1.033)
P2 = 86 kPa * 0.7957
P2 ≈ 68.5112 kPa
The pressure of the gas in the second container is approximately 68.5 kPa. Therefore, the correct answer is none of these, as none of the given options match the result we obtained.