A gas sample with a volume of 5.3L has a pressure of 745mmHg at 33degrees C.What is the pressure of the sample if the volume remains at 5.3L but the temperature rises to 79degres C?
(P1/T1) = (P2/T2)
Remember T must be in kelvin.
To solve this problem, we can use the combined gas law, which relates the pressure, volume, and temperature of a gas sample. The combined gas law can be expressed as:
(P1 * V1) / T1 = (P2 * V2) / T2
Where:
P1 = initial pressure
V1 = initial volume
T1 = initial temperature
P2 = final pressure (unknown)
V2 = final volume (same as V1)
T2 = final temperature
Now let's plug in the given values into the formula:
(P1 * V1) / T1 = (P2 * V2) / T2
P1 = 745 mmHg
V1 = 5.3 L
T1 = 33 degrees Celsius = 33 + 273.15 = 306.15 K
V2 = 5.3 L
T2 = 79 degrees Celsius = 79 + 273.15 = 352.15 K
Now, rearranging the formula to solve for P2:
P2 = (P1 * V1 * T2) / (V2 * T1)
Plugging in the values:
P2 = (745 mmHg * 5.3 L * 352.15 K) / (5.3 L * 306.15 K)
P2 ≈ 917 mmHg
Therefore, the pressure of the sample when the volume remains at 5.3 L but the temperature rises to 79 degrees Celsius is approximately 917 mmHg.
To solve this problem, we can use the Ideal Gas Law, which states that PV = nRT, where P is the pressure, V is the volume, n is the number of moles of the gas, R is the ideal gas constant, and T is the temperature in Kelvin.
First, let's convert the temperatures from degrees Celsius to Kelvin. We add 273.15 to each Celsius temperature to get the Kelvin temperature.
Given:
Initial volume, V1 = 5.3 L
Initial pressure, P1 = 745 mmHg
Initial temperature, T1 = 33 °C = 33 + 273.15 = 306.15 K
We want to find the final pressure, P2, when the temperature, T2, changes to 79 °C = 79 + 273.15 = 352.15 K.
Since the volume remains constant, the number of moles of the gas (n) and the volume (V) are constant. Therefore, we can rewrite the Ideal Gas Law equation as:
P1/T1 = P2/T2
Now, we can plug in the given values:
745 mmHg / 306.15 K = P2 / 352.15 K
To find P2, we can cross-multiply and solve for P2:
P2 = (745 mmHg * 352.15 K) / 306.15 K
P2 ≈ 855.59 mmHg
Therefore, the pressure of the gas sample when the temperature rises to 79 °C is approximately 855.59 mmHg.