New preesure when 2 containers are connected

[darkar]

Here is the question:
Two gas containers with volumes of 100 cm3 and 1000cm3 respectively are connected by a tube of negligible volume, and contain air at a pressure of 1000 mm Hg. If the temperature of both vessels is originally 273 K, what is the new pressure when the temperature of the smaller is raised to 373 K?

Answer : 1025 mm Hg

How are u going to work this out this quetion? and please give some comment on my working.

I got my answers correct but i have a little doubt on my working,
i used
initial PV/T + PV/T = final PV/T + PV/T since mass is conserved.

Thx.

 

[member 553083]

Your approach is correct. The ideal gas law states that PV = nRT, where P is pressure, V is volume, n is the number of moles of the gas, R is the ideal gas constant and T is temperature. Since the number of moles of gas remains constant, the equation can be written as P1V1/T1 = P2V2/T2. By rearranging this equation, we get P2 = (P1V1/T1) x (T2/V2). Since the volume of the tube is negligible, all the gas is confined to the two vessels, so P2 = (1000 mmHg)(100 cm3)/273 K x (373K/1000cm3) = 1025 mmHg.

 

[wais]

To solve this question, we can use the ideal gas law, which states that the product of pressure (P) and volume (V) is directly proportional to the absolute temperature (T) and the number of moles (n) of gas. Mathematically, this can be represented as PV = nRT, where R is the gas constant.

In this scenario, the number of moles and gas constant remain constant. Therefore, we can use the formula P1V1/T1 = P2V2/T2 to calculate the new pressure when the temperature of the smaller container is raised to 373 K.

Using this formula, we can plug in the initial values for pressure (1000 mm Hg), volume (100 cm3), and temperature (273 K) for the larger container and the new temperature (373 K) for the smaller container. This gives us:

P1V1/T1 = P2V2/T2
(1000 mm Hg)(100 cm3)/(273 K) = P2(1000 cm3)/(373 K)

Solving for P2, we get:
P2 = (1000 mm Hg)(100 cm3)(373 K)/(1000 cm3)(273 K)
P2 = 1025 mm Hg

Therefore, the new pressure when the temperature of the smaller container is raised to 373 K is 1025 mm Hg.

Your working is correct, but it would be helpful to show your calculations step by step to make it easier to follow. Also, it is important to label your units (mm Hg, cm3, K) to avoid confusion. Overall, good job on getting the correct answer! Keep practicing and you will become more confident in solving these types of problems.