To find the total pressure exerted by the gases in the gas cylinder, we will use Dalton's Law of Partial Pressures. This law states that the total pressure exerted by a mixture of non-reacting gases is equal to the sum of the partial pressures of the individual gases. Mathematically, this can be expressed as:
[tex]\[ P_T = P_{N_2} + P_{O_2} + P_{Ar} + P_{He} + P_{H} \][/tex]
Given the partial pressures:
- [tex]\( P_{N_2} = 3.00 \, \text{atm} \)[/tex]
- [tex]\( P_{O_2} = 1.80 \, \text{atm} \)[/tex]
- [tex]\( P_{Ar} = 0.29 \, \text{atm} \)[/tex]
- [tex]\( P_{He} = 0.18 \, \text{atm} \)[/tex]
- [tex]\( P_{H} = 0.10 \, \text{atm} \)[/tex]
We add these pressures together to find the total pressure:
[tex]\[ P_T = 3.00 \, \text{atm} + 1.80 \, \text{atm} + 0.29 \, \text{atm} + 0.18 \, \text{atm} + 0.10 \, \text{atm} \][/tex]
Adding these values step-by-step:
[tex]\[ 3.00 + 1.80 = 4.80 \][/tex]
[tex]\[ 4.80 + 0.29 = 5.09 \][/tex]
[tex]\[ 5.09 + 0.18 = 5.27 \][/tex]
[tex]\[ 5.27 + 0.10 = 5.37 \][/tex]
So, the total pressure exerted by the gases is:
[tex]\[ 5.37 \, \text{atm} \][/tex]
Therefore, the correct answer is:
[tex]\[ \boxed{5.37 \, \text{atm}} \][/tex]
