What volume in liters would contain 5.30 x 10^24 molecules of hydrogen gas at STP?
To calculate the volume in liters that would contain a certain number of molecules of a gas at STP (Standard Temperature and Pressure), you can use the ideal gas law equation:
PV = nRT
Where:
P = pressure (in atmospheres)
V = volume (in liters)
n = number of moles of gas
R = ideal gas constant (0.0821 L·atm/(mol·K))
T = temperature (in Kelvin)
At STP, the temperature is 273.15 K, and the pressure is 1 atm. Also, 1 mole of gas contains 6.022 x 10^23 molecules (Avogadro's number).
First, we need to find the number of moles of hydrogen gas given the number of molecules. We can use Avogadro's number to convert the number of molecules to moles:
Number of moles = number of molecules / Avogadro's number
Number of moles = (5.30 x 10^24) / (6.022 x 10^23)
Number of moles ≈ 8.80
Now, we can plug in the values and solve for V:
(1 atm) * V = (8.80 mol) * (0.0821 L·atm/(mol·K)) * (273.15 K)
V ≈ 22.4 L
Therefore, a volume of approximately 22.4 liters would contain 5.30 x 10^24 molecules of hydrogen gas at STP.