What is the pressure of the gas, in atmosphere, inside the cylinder?

Question

Ten moles of Hydrogen gas at 0°C are forced into a steel cylinder with a volume of 200 mL. What is the pressure of the gas, in atmosphere, inside the cylinder?

Please help me solving this problem step by step...thanks

Answer 1

Not that many steps to use.
At 1 Atm, the 10 moles would occupy 224 liters.
You're compressing the size to 200 ml (0.2 liters).
As an ideal gas, the pressure increases inversely to this compression. So it would be 224/0.2 atm or 1120 atm.

BTW: I doubt if hydrogen would be an ideal gas at 1120 atm, but that's another story.

Answer 2

PV=nRT

you are looking for pressure so P is your unknown
T=0+273 because you must be in kelvin
n=10 moles
V= 200mL but must be converted to .2 L
R= is the gas constant and there are many diffrent versions the one you want is 0.0820578437 L · atm · K-1 · mol-1
as you can see, the units of everything else matches with the units of the gas constant. When you plug the values into the formula you get your answer
P=((0.0820578437 L · atm · K-1 · mol-1)(10 mol)(273K))/.2 L
Everything cancels out and you will be left with a pressure in atm.