At 10°C, the gas in a cylinder has a volume of 0.250 L. The gas is allowed to expand to 0.285 L.
What must the final temperature be for the pressure to remain constant? (Hint °C + 273 = K.)
248 K
284 K
323 K
282 K
To solve this problem, we can use the ideal gas law, which states:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles
R = gas constant
T = temperature
Since the pressure is constant, we can simplify the equation to:
V1/T1 = V2/T2
Where:
V1 = initial volume
T1 = initial temperature
V2 = final volume
T2 = final temperature
Plugging in the given values:
V1 = 0.250 L
T1 = 10°C + 273 = 283 K
V2 = 0.285 L
Now we can solve for T2:
0.250/283 = 0.285/T2
Cross-multiplying, we get:
0.250T2 = 0.285 * 283
0.250T2 = 80.955
T2 = 80.955/0.250
T2 ≈ 323.82
Rounding to the nearest whole number, the final temperature must be approximately 323 K.
Therefore, the correct answer is 323 K.
are you sure
Apologies for the confusion in my previous response. Let's solve the problem correctly.
By using the formula V1/T1 = V2/T2 and plugging in the given values:
V1 = 0.250 L
T1 = 10°C + 273 = 283 K
V2 = 0.285 L
We have:
0.250/283 = 0.285/T2
Cross-multiplying, we get:
0.250T2 = 0.285 * 283
0.250T2 = 80.655
Finally, solving for T2:
T2 = 80.655/0.250
T2 ≈ 322.62
Rounding to the nearest whole number, the final temperature must be approximately 323 K.
Therefore, the correct answer is 323 K.