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138. You have two rigid gas cylinders. Gas cylinder A has a volume of 48.2 L and contains N2(g) at 8.35 atm at 25 °C. Gas cylinder B has a volume of 22.0 L and contains He(g) at 25 °C. When the two cylinders are connected with a valve of negligible volume and the gases are mixed, the pressure in each cylinder becomes 8.71 atm. (Assume no reaction when the gases are mixed.)a. How many nitrogen molecules are present?b. What is the total number of moles of N2(g) and He(g) present after the gases are mixed?c. What was the beginning pressure of cylinder B containing only the He(g) (i.e., before the valve was connected)?d. Think about the He(g) before and after the cylinders were connected. Graph the relationship between pressure and volume (without numbers) for the He(g) showing this change, and explain your answer, making sure to address the variables P, V, n, and T.

Question

138. You have two rigid gas cylinders. Gas cylinder A has a volume of 48.2 L and contains N2(g) at 8.35 atm at 25 °C. Gas cylinder B has a volume of 22.0 L and contains He(g) at 25 °C. When the two cylinders are connected with a valve of negligible volume and the gases are mixed, the pressure in each cylinder becomes 8.71 atm. (Assume no reaction when the gases are mixed.)

a. How many nitrogen molecules are present?

b. What is the total number of moles of N2(g) and He(g) present after the gases are mixed?

c. What was the beginning pressure of cylinder B containing only the He(g) (i.e., before the valve was connected)?

d. Think about the He(g) before and after the cylinders were connected. Graph the relationship between pressure and volume (without numbers) for the He(g) showing this change, and explain your answer, making sure to address the variables P, V, n, and T.

 

check_circleAnswer
Step 1

Given:

Volume of gas (VN2) = 48.2 L.

Pressure of gas (PN2) = 8.35 atm.

Temperature of gas (TN2) = 25℃ = 298 K.

Volume of gas (VHe) = 22.0 L.

Temperature of gas (THe) = 25℃ = 298 K.

Total pressure when gasses are mixed = 8.71 atm.

Step 2

Calculation for number of molecules of N2 in cylinder A:

PV
n x R xT
PN2 VN2
nN2 X R X TN2
8.35 atm X 48.2 L
nN2 X 0.0821 atm. L/K. mol x 298K
402.47 nN2 X 24.47 mol-1
16.45 moles.
nN2
6.023 x 1023 molecules
since, 1 mole
16.45 x 6.023 x 1023 molecules
Therefore, 16.45 moles
= 99.078 x 1023 molecules.
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Image Transcriptionclose

PV n x R xT PN2 VN2 nN2 X R X TN2 8.35 atm X 48.2 L nN2 X 0.0821 atm. L/K. mol x 298K 402.47 nN2 X 24.47 mol-1 16.45 moles. nN2 6.023 x 1023 molecules since, 1 mole 16.45 x 6.023 x 1023 molecules Therefore, 16.45 moles = 99.078 x 1023 molecules.

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Step 3

Calculation for total number of moles:

After mixing both the gases:

PT = 8.71 atm.

VT = VN2 + VHe = 48.2 +22.0 = 70.2 L.

TT...

Pr Vт — Пт XR х T
nт х0.0821 atm. L/K. molx 298 K
8.71 atm X 70.2 L
611.45
E Пт X 24.47 mol-1.
24.98 moles
Пт
help_outline

Image Transcriptionclose

Pr Vт — Пт XR х T nт х0.0821 atm. L/K. molx 298 K 8.71 atm X 70.2 L 611.45 E Пт X 24.47 mol-1. 24.98 moles Пт

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