To determine the number of moles of chlorine gas (Cl2) occupying a volume of 15.7 liters at standard temperature and pressure (STP), we can utilize two different methods based on the properties of ideal gases.
The first method involves using the standard molar volume of an ideal gas, which is 22.4 liters per mole at STP. By applying this conversion factor, we can calculate the moles of Cl2 as follows:
Number of moles = Volume (liters) / Molar volume (liters/mole) = 15.7 L / 22.4 L/mol
When we perform this calculation, we find that:
Number of moles = 0.70 moles of Cl2
Alternatively, we can use the ideal gas law, represented by the equation:
PV = nRT
Where:
- P = pressure (1 atmosphere at STP)
- V = volume (15.7 liters)
- n = number of moles
- R = ideal gas constant (0.0821 L·atm/(K·mol))
- T = temperature (273.15 Kelvin at STP)
Rearranging the equation to solve for n gives us:
n = PV / RT
Substituting the known values:
n = (1 atm) * (15.7 L) / (0.0821 L·atm/(K·mol) * 273.15 K)
Upon calculating this, we also arrive at:
n = 0.70 moles of Cl2
Both methods yield the same result, demonstrating that we can effectively determine the number of moles of a gas at STP either through the standard molar volume or by applying the ideal gas law.
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