A gas sample a of 2.45 atm when the temperature is - 19 deg C What is the final pressure, in atmospheres, when the temperature is 45 deg C with no change in the volume or amount of gas? Express your answer with the appropriate units.
To solve this problem, we can use the combined gas law:
(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 (which remain constant in this problem), and T1 and T2 are the initial and final temperatures.
Given:
P1 = 2.45 atm
T1 = -19 °C = 254 K
T2 = 45 °C = 318 K
Rearranging the formula, we have:
P2 = (P1 * T2 * V1) / (T1 * V2)
Substituting the given values:
P2 = (2.45 atm * 318 K * V1) / (254 K * V2)
Since the volume (V1 and V2) remains constant, we can cancel them out in the equation:
P2 = (2.45 atm * 318 K) / 254 K
Calculate:
P2 = 3.07 atm
Therefore, the final pressure when the temperature is 45 °C is 3.07 atm.
To solve this problem, we can use the combined gas law, which relates the initial and final pressures and temperatures of a gas sample when there is no change in volume or amount of gas.
The combined gas law equation is:
(P1 * V1) / (T1) = (P2 * V2) / (T2)
Where:
P1 = initial pressure
V1 = initial volume (constant in this case)
T1 = initial temperature
P2 = final pressure (what we need to determine)
V2 = final volume (constant in this case)
T2 = final temperature
Given values:
P1 = 2.45 atm
T1 = -19°C = 254 K
T2 = 45°C = 318 K
Using the combined gas law equation, we can rearrange it to solve for P2:
P2 = (P1 * V1 * T2) / (V2 * T1)
Since there is no change in volume, V1 = V2, and we can simplify the equation to:
P2 = (P1 * T2) / T1
Now we can substitute the given values into the equation:
P2 = (2.45 atm * 318 K) / 254 K
Calculating this equation:
P2 = 3.07 atm
Therefore, the final pressure, when the temperature is 45°C with no change in the volume or amount of gas, is approximately 3.07 atm.
To find the final pressure of the gas sample, we can make use of the combined gas law, which relates the initial and final pressures, volumes, and temperatures. The combined gas law is represented as:
(P1 * V1) / (T1) = (P2 * V2) / (T2)
Where:
P1 is the initial pressure
V1 is the initial volume
T1 is the initial temperature
P2 is the final pressure (what we're trying to find)
V2 is the final volume (it remains the same in this case)
T2 is the final temperature
In this case, we know that:
P1 = 2.45 atm
T1 = -19 °C = -19 + 273.15 K = 254.15 K
V1 = V2 (no change in volume)
T2 = 45 °C = 45 + 273.15 K = 318.15 K
Now let's plug in these values into the combined gas law equation:
(2.45 * V1) / 254.15 = (P2 * V1) / 318.15
Since V1 is common to both sides, we can cancel it out:
2.45 / 254.15 = P2 / 318.15
Now we can solve for P2:
P2 = (2.45 / 254.15) * 318.15
P2 ≈ 3.052 atm
So the final pressure of the gas sample, when the temperature is 45°C and there is no change in volume or amount of gas, is approximately 3.052 atm.