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Five gases combined in a gas cylinder have the following partial pressures:

[tex]\[ 3.00 \, \text{atm} \, (N_2), \, 1.80 \, \text{atm} \, (O_2), \, 0.29 \, \text{atm} \, (Ar), \, 0.18 \, \text{atm} \, (He), \, \text{and} \, 0.10 \, \text{atm} \, (H_2). \][/tex]

What is the total pressure exerted by the gases? Use the formula:

[tex]\[ P_T = P_1 + P_2 + P_3 + \ldots + P_n \][/tex]

A. [tex]\( 5.08 \, \text{atm} \)[/tex]
B. [tex]\( 5.19 \, \text{atm} \)[/tex]
C. [tex]\( 5.27 \, \text{atm} \)[/tex]
D. [tex]\( 5.37 \, \text{atm} \)[/tex]



Answer :

GinnyAnswer
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]

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