When the temperature of a rigid hollow sphere containing 685 L of helium gas is held at 621 K, the pressure of the gas is #1.89*10^3# kPa. How many moles of helium does the sphere contain?

Question

Wyatt Adkins · Accepted Answer

#"251 moles"#

You must use the ideal gas law equation to determine how many moles of gas are present in that helium sample at those pressure and temperature levels.

#color(blue)(|bar(ul(color(white)(a/a)PV = nRTcolor(white)(a/a)|)))" "#, where

#P# - the pressure of the gas #V# - the volume it occupies #n# - the number of moles of gas #R# - the universal gas constant, usually given as #0.0821("atm" * "L")/("mol" * "K")# #T# - the absolute temperature of the gas

Now, confirm that the pressure, temperature, and volume units you were given match the units used in the universal gas constant expression before entering your values into the ideal gas law equation.

As you can see, #R# uses atm as the unit for pressure. The problem gives you the pressure of the gas expressed in kPa. This means that you're going to have to convert the pressure from kPa to atm by using the conversion factor

#color(purple)(|bar(ul(color(white)(a/a)color(black)("1 atm" = 1.01325 * 10^3"kPa")color(white)(a/a)|)))#

The units for volume and temperature match those used by #R#, so rearrange the ideal gas law equation to solve for #n#

#PV = nRT implies n = (PV)/(RT)#

Enter your values to obtain

#n = ((1.89 * 10^3color(red)(cancel(color(black)("atm"))))/(1.01325 * 10^2color(red)(cancel(color(black)("atm")))) * 685color(red)(cancel(color(black)("L"))))/(0.0821(color(red)(cancel(color(black)("atm"))) * color(red)(cancel(color(black)("L"))))/("mol" * color(red)(cancel(color(black)("K")))) * 621color(red)(cancel(color(black)("K")))) = "250.61 moles"#

The response, rounded to three sig figs, is

#n = color(green)(|bar(ul(color(white)(a/a)"251 moles" color(white)(a/a)|)))#

Wyatt Adkins · Answer

undefined The sphere contains approximately 90.3 moles of helium gas.