The question has been answered years ago but not how it is solved. I tried the combined gas law. Here is the question: A balloon originally had a volume of 4.39 L at 44 degrees celsius and a pressure of 729 torr. The balloon must be cooled ??? to reduce its volume to 3.78 L at constant pressure.
I used T2= P2*V2*T1/ P1*V1
Please help me understand why it is zero degrees!
First since it is constant P you don't need the P1 and P2 so the equation can be modified to T2 = V2T1/T2 although you could use your formula and just use 729 for P1 and 729 for P2.
V2 is 3.78L
V1 is 4.39L
T1 is 44 C which is (273+44) = 317 Kelvin.
Substitute into the equation for
3.78*317/4.39 = 272.95K and that rounds to 273 K. To convert to C, that is
K = 273+C or 273-273 = zero Celsius.
To understand why the temperature needs to be zero degrees Celsius, let's analyze the problem using the combined gas law, as you mentioned.
The combined gas law states that the ratio between the initial and final conditions of pressure (P), volume (V), and temperature (T) is constant, as long as the number of moles and the gas remains constant.
The equation you used, T2 = (P2 * V2 * T1) / (P1 * V1), is the correct form of the combined gas law equation.
Let's plug in the given values for the initial conditions:
P1 = 729 torr
V1 = 4.39 L
T1 = 44 °C + 273.15 (converting to Kelvin) = 317.15 K
And the desired values for the final conditions:
V2 = 3.78 L
Now, let's solve for T2:
T2 = (P2 * V2 * T1) / (P1 * V1)
Since the problem states that the pressure remains constant, we can substitute the given and desired pressures (P1 = P2 = 729 torr). Therefore, the pressure cancels out in the equation.
T2 = (729 torr * 3.78 L * 317.15 K) / (729 torr * 4.39 L)
The L units also cancel, giving:
T2 = (3.78 * 317.15) / 4.39 K
T2 = 273.47 K
Now, converting back to Celsius, we subtract 273.15:
T2 = 273.47 K - 273.15
T2 ≈ 0.32 °C
Therefore, cooling the balloon to approximately 0 degrees Celsius would reduce its volume to 3.78 L at constant pressure.
It's important to note that while the answer is close to zero, it may not be exactly zero due to rounding and the precision of the data.