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? 1400mL
To calculate the final temperature of the gas, we can use the combined gas law equation. The combined gas law equation relates the initial and final conditions of a gas when pressure, volume, and temperature change, while the amount of gas remains constant.
The equation is given as:
(P₁ * V₁) / T₁ = (P₂ * V₂) / T₂
Where:
P₁ = initial pressure
V₁ = initial volume
T₁ = initial temperature
P₂ = final pressure
V₂ = final volume
T₂ = final temperature
In this case, the initial volume (V₁) is 4.40L at 0∘C and the final volume (V₂) is 1400mL. The initial temperature (T₁) is 0∘C, and we need to find the final temperature (T₂).
First, let's convert the final volume from mL to L:
1400 mL = 1400/1000 = 1.4 L
Plugging the given values into the equation, we have:
(P₁ * 4.40L) / (0∘C + 273.15) = (P₂ * 1.4L) / (T₂ + 273.15)
Since the problem states that the pressure (P) and the amount of gas (n) are constant, we can ignore them in our calculation, making the equation:
(4.40L) / (0∘C + 273.15) = (1.4L) / (T₂ + 273.15)
Now, let's solve for T₂:
Cross multiply the equation:
(4.40L) * (T₂ + 273.15) = (1.4L) * (0∘C + 273.15)
Distribute and simplify the equation:
4.40L * T₂ + 4.40L * 273.15 = 1.4L * 273.15
Rearrange the equation to isolate T₂:
4.40L * T₂ = 1.4L * 273.15 - 4.40L * 273.15
T₂ = (1.4L * 273.15 - 4.40L * 273.15) / 4.40L
Simplifying further:
T₂ = (1.4 - 4.40) * 273.15
T₂ = (-3.0) * 273.15
T₂ = -819.45
The final temperature, T₂, is -819.45 degrees Celsius.
Note: It's not physically possible to have a negative temperature in degrees Celsius. Please double-check the given values and the calculations to ensure accuracy.
To find the final temperature needed to change the volume of the gas to 1400 mL, we can use the combined gas law which states:
(P1 * V1) / (T1) = (P2 * V2) / (T2)
Given:
V1 = 4.40 L
T1 = 0°C (273.15K)
V2 = 1400 mL (convert to L by dividing by 1000) = 1.40 L
P1 and P2 are not given, but since the problem states that the pressure (P) does not change, we can assume that P1 = P2.
Let's plug in the values into the combined gas law equation:
(P1 * V1) / T1 = (P2 * V2) / T2
(P * 4.40L) / (273.15K) = (P * 1.40L) / (T2)
Simplifying further:
(4.40L) / (273.15K) = (1.40L) / (T2)
Cross multiplying:
(1.40L) * (273.15K) = (4.40L) * (T2)
382.41 = 19.36 * T2
Dividing both sides by 19.36:
T2 = 382.41 / 19.36
T2 = 19.74°C
Therefore, the final temperature needed to change the volume of the gas to 1400 mL is approximately 19.74°C.
(V1/T1) = (V2/T2)
Remember T must be in kelvin.