First, let's understand that standard temperature and pressure (STP) conditions refer to a temperature of 0°C and a pressure of 1 atm. Under these conditions, one mole of any ideal gas occupies a volume of 22.4 liters.
We need to find out the volume each gas occupies at STP, then determine which gas occupies the highest volume.
1. Volume of [tex]\( O_2 \)[/tex] at STP:
- Given: [tex]\( 0.02 \)[/tex] moles of [tex]\( O_2 \)[/tex]
- Volume = Number of moles × Volume per mole at STP
- Volume of [tex]\( O_2 = 0.02 \)[/tex] moles × 22.4 liters/mole
- Volume of [tex]\( O_2 = 0.448 \)[/tex] liters
2. Volume of [tex]\( Cl_2 \)[/tex] at STP:
- Given: [tex]\( 0.1 \)[/tex] moles of [tex]\( Cl_2 \)[/tex]
- Volume = Number of moles × Volume per mole at STP
- Volume of [tex]\( Cl_2 = 0.1 \)[/tex] moles × 22.4 liters/mole
- Volume of [tex]\( Cl_2 = 2.24 \)[/tex] liters
3. Volume of [tex]\( N_2 \)[/tex] at STP:
- Given: [tex]\( 1 \)[/tex] mole of [tex]\( N_2 \)[/tex]
- Volume = Number of moles × Volume per mole at STP
- Volume of [tex]\( N_2 = 1 \)[/tex] mole × 22.4 liters/mole
- Volume of [tex]\( N_2 = 22.4 \)[/tex] liters
4. Volume of [tex]\( H_2 \)[/tex] at STP:
- Given: [tex]\( 2 \)[/tex] moles of [tex]\( H_2 \)[/tex]
- Volume = Number of moles × Volume per mole at STP
- Volume of [tex]\( H_2 = 2 \)[/tex] moles × 22.4 liters/mole
- Volume of [tex]\( H_2 = 44.8 \)[/tex] liters
Now, let’s compare the volumes of these gases to determine which one occupies the highest volume:
- Volume of [tex]\( O_2 = 0.448 \)[/tex] liters
- Volume of [tex]\( Cl_2 = 2.24 \)[/tex] liters
- Volume of [tex]\( N_2 = 22.4 \)[/tex] liters
- Volume of [tex]\( H_2 = 44.8 \)[/tex] liters
From the volumes calculated, [tex]\( H_2 \)[/tex] occupies the highest volume at STP, which is 44.8 liters. Therefore, the gas that occupies the highest volume at STP is [tex]\( 2 \)[/tex] moles of [tex]\( H_2 \)[/tex].
