Container A holds 737 mL of ideal gas at 2.30 atm. Container B holds 114 mL of ideal gas at 4.40 atm. lf the gases are allowed to mix together, what is the resulting pressure?

Question

Luna Chen · Accepted Answer

The resulting pressure is 2.58 atm.

According to Dalton's Law of Partial Pressures, each gas will exert its pressure independently of the other. Hence we can use Boyle's Law to calculate the pressure of each gas separately as it expands into the total volume of the two containers. Calculate the pressure of Gas A Boyle's Law is #color(blue)(bar(ul(|color(white)(a/a)p_1V_1 = p_2V_2color(white)(a/a)|)))" "# #p_1 = "2.30 atm"; color(white)(l)V_1= "737 mL"# #p_2 = "?";color(white)(mmmm) V_2 = "737 mL + 114 mL" = "851 mL"# #p_2 = p_1 × V_1/V_2 = "2.30 atm" × (737 color(red)(cancel(color(black)("mL"))))/(851 color(red)(cancel(color(black)("mL")))) = "1.992 atm"# Calculate the pressure of Gas B #p_1 = "4.40 atm"; color(white)(l)V_1= "114 mL"# #p_2 = "?";color(white)(mmmm) V_2 = "114 mL + 737 mL" = "851 mL"# #p_2 = p_1 × V_1/V_2 = "4.40 atm" × (114 color(red)(cancel(color(black)("mL"))))/(851 color(red)(cancel(color(black)("mL")))) = "0.5894 atm"# Calculate the total pressure The formula for Dalton's Law of Partial Pressures is #color(blue)(bar(ul(|color(white)(a/a)p_"tot" = p_"A" + p_"B"color(white)(a/a)|)))" "# #p_"tot" = "1.992 atm + 0.5894 atm" = "2.58 atm"#

Naomi Aronson · Answer

undefined To find the resulting pressure when the gases are mixed together, you can use Dalton's Law of Partial Pressures. According to Dalton's Law, the total pressure of a mixture of gases is equal to the sum of the partial pressures of each individual gas.

So, $ P_{\text{total}} = P_{\text{A}} + P_{\text{B}} $, where $ P_{\text{A}} $ and $ P_{\text{B}} $ are the partial pressures of gases A and B, respectively.

To find the partial pressures, use the formula $ P = \frac{nRT}{V} $, where $ P $ is pressure, $ n $ is the number of moles of gas, $ R $ is the ideal gas constant, $ T $ is the temperature in Kelvin, and $ V $ is the volume.

First, find the number of moles of gas in each container using the ideal gas law: $ n = \frac{PV}{RT} $.

Then, calculate the partial pressures of gases A and B.

Finally, add the partial pressures together to find the total pressure.