A #5 L# container holds #7 # mol and #4 # mol of gasses A and B, respectively. Groups of four of molecules of gas B bind to three molecule of gas A and the reaction changes the temperature from #250^oK# to #370 ^oK#. By how much does the pressure change?

Question

A #5 L# container holds #7 # mol and #4 # mol of gasses A and B, respectively.  Groups of four of molecules of gas B bind to three molecule of gas A and the reaction changes the temperature from #250^oK# to #370 ^oK#. By how much does the pressure change?

Charlotte Aaron · Accepted Answer

It decreases by 32.7%

This is really chemistry question, although it does overlap with the physics topic indicated. Volume is directly related to molar amounts, temperature and pressure according to the Ideal Gas Law: #P*V = (n*R*T)# The change in molar amounts is derived from the balanced chemical equation. 7A + 4B → A_3B_4 + 4A (unreacted) So, we initially have 11 moles of gases and end up with 5 moles in the 5L volume. The volume is constant in this case, and the gas constant is constant, so we only need the equation that shows the change in pressure with respect to molar quantities (n) and temperature (T) for a calculation of the ratio change. #P_2/ P_1 = (n_2/n_1) xx (T_2/T_1)# #P_2/ P_1 = (5/11) xx (370/250)# ; #P_2/ P_1 = 0.673# So, the pressure decreases by #1 – 0.673 = 0.327# or 32.7%

Layla Ahmed · Answer

undefined To find the change in pressure, we can use the ideal gas law, which states:

PV = nRT

Where:
- P is the pressure
- V is the volume
- n is the number of moles
- R is the ideal gas constant
- T is the temperature in Kelvin

Since the volume (V) and the number of moles (n) remain constant, we can rewrite the equation as:

P1/T1 = P2/T2

Where:
- P1 and T1 are the initial pressure and temperature, respectively.
- P2 and T2 are the final pressure and temperature, respectively.

Given:
- Initial temperature (T1) = 250 K
- Final temperature (T2) = 370 K

We need to calculate the initial and final pressures, P1 and P2.

For initial pressure (P1), we use the given data to find the initial number of moles of gas A and gas B:
- Moles of gas A = 7 mol
- Moles of gas B = 4 mol

Since 4 molecules of gas B bind to 3 molecules of gas A, the number of molecules involved in the reaction is determined by the limiting reactant, which is gas A. So, we use the moles of gas A for our calculation.

Next, we need to determine the total number of molecules in the initial state. Since 4 molecules of gas B bind to 3 molecules of gas A, and there are 7 moles of gas A, we have:

Total number of molecules = 7 moles × Avogadro's number

Once we have the total number of molecules, we can calculate the initial pressure (P1) using the ideal gas law.

For final pressure (P2), we repeat the same process using the final temperature (370 K).

After finding both initial and final pressures, we can use the formula P1/T1 = P2/T2 to find the change in pressure.

Let's perform the calculations:
- Initial number of molecules = 7 moles × Avogadro's number
- Initial pressure (P1) = (nRT) / V
- Final pressure (P2) = (nRT) / V
- Change in pressure = P2 - P1