A sample of gas at 47°C and 1.03 atm occupies a volume of 2.20L. What volume would this gas occupy at 107°C and 0.789 atm? Does your answer make sense in terms of the gas law relationships?
PV=kT, so you want V such that
0.789V/(273+107) = 1.03*2.20/(273+47)
the question about making sense seems kind of unnecessary, since the only way to arrive at the answer would be to use the gas laws.
However, whenever you solve a problem, a sanity check on the answer should always be done.
To answer this question, we can use the combined gas law, which states that the product of pressure and volume divided by temperature is constant for a given amount of gas. The equation can be written as:
(P1 * V1) / T1 = (P2 * V2) / T2
Where:
P1 and P2 are the initial and final pressures,
V1 and V2 are the initial and final volumes, and
T1 and T2 are the initial and final temperatures.
Let's plug in the given values:
P1 = 1.03 atm
V1 = 2.20 L
T1 = 47°C + 273.15 = 320.15 K (temperature must be in Kelvin)
P2 = 0.789 atm
V2 = ? (this is what we're trying to find)
T2 = 107°C + 273.15 = 380.15 K
Now we can rearrange the equation to solve for V2:
(P1 * V1 * T2) / (T1 * P2) = V2
Plugging in the values:
V2 = (1.03 atm * 2.20 L * 380.15 K) / (320.15 K * 0.789 atm)
Simplifying the equation:
V2 = 2.49 L
So the gas would occupy a volume of approximately 2.49 liters at 107°C and 0.789 atm.
Now, let's consider if the answer makes sense in terms of the gas law relationships. According to Charles's Law, the volume of a gas is directly proportional to its temperature at constant pressure, assuming the pressure and amount of gas remain constant. In this case, the temperature increased from 47°C to 107°C, and we would expect the volume to increase accordingly. Since the calculated volume at the higher temperature is indeed larger than the initial volume, the answer aligns with the gas law relationships.