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?
1 Answer
Explanation:
In order to find the number of moles of gas present in that sample of helium under those conditions for pressure and temperature, you must use the ideal gas law equation
#color(blue)(|bar(ul(color(white)(a/a)PV = nRTcolor(white)(a/a)|)))" "# , where
Now, before plugging in your values into the ideal gas law equation, make sure that the units given to you for pressure, temperature, and volume match the units used in the expression of the universal gas constant.
As you can see,
#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
#PV = nRT implies n = (PV)/(RT)#
Plug in your values to get
#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"#
Rounded to three sig figs, the answer will be
#n = color(green)(|bar(ul(color(white)(a/a)"251 moles" color(white)(a/a)|)))#