A gas has a volume of 4.40L at 0∘C. What final temperature, in degrees Celsius, is needed to change the volume of the gas to each of the following, if P and n do not change?
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A gas has a volume of 4.00 L at 0 oC. What final temperature, in degrees Celsius, is needed to change the volume of the gas to each of the following, if amount and pressure do not change
To solve this problem, we can use the combined gas law equation:
(P1 * V1) / (T1) = (P2 * V2) / (T2)
Given:
Initial volume (V1) = 4.40 L
Initial temperature (T1) = 0 °C = 273.15 K (convert to Kelvin)
Now we can calculate the final temperatures for different volumes:
1) Final volume (V2) = 2.20 L:
Calculate the final temperature (T2) using the combined gas law equation:
(P1 * V1) / T1 = (P2 * V2) / T2
T2 = (P2 * V2 * T1) / (P1 * V1)
Assume the pressure (P1 and P2) and the number of moles (n) remain constant.
T2 = (P2 * V2 * T1) / (P1 * V1)
= (P2 * 2.20 L * 273.15 K) / (P1 * 4.40 L)
2) Final volume (V2) = 8.80 L:
Calculate the final temperature (T2) using the same formula.
T2 = (P2 * V2 * T1) / (P1 * V1)
= (P2 * 8.80 L * 273.15 K) / (P1 * 4.40 L)
Repeat the steps above for each final volume to find the respective final temperatures.
To find the final temperature needed to change the volume of the gas, we can use the combined gas law equation, which relates the initial and final conditions of the gas. The combined gas law equation is given as:
(P1 * V1)/T1 = (P2 * V2)/T2
Where:
P1 = initial pressure (not changing)
V1 = initial volume (4.40L in this case)
T1 = initial temperature (0°C in this case)
P2 = final pressure (not changing)
V2 = final volume (the volume we want to find)
T2 = final temperature (what we need to calculate)
Based on the given information, the values that do not change are the pressure (P) and the number of moles (n). Therefore, we can simplify the equation as:
V1/T1 = V2/T2
Now, we can rearrange the equation to solve for T2:
T2 = (V2 * T1) / V1
Substituting the known values:
V1 = 4.40L (initial volume)
T1 = 0°C (initial temperature)
Let's say we want to change the volume of the gas to a final volume of 6.60L.
Plugging in the values, we have:
T2 = (6.60L * 0°C) / 4.40L
Simplifying the equation:
T2 = 0°C
So, if the volume changes from 4.40L to 6.60L while keeping the pressure and number of moles constant, the final temperature required to achieve this change would remain at 0°C.