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Which gas occupies the highest volume at STP?

A. 0.02 mol of [tex]\( O_2 \)[/tex]
B. 0.1 mol of [tex]\( Cl_2 \)[/tex]
C. 1 mol of [tex]\( N_2 \)[/tex]
D. 2 mol of [tex]\( H_2 \)[/tex]

Sagot :

GinnyAnswer
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].
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