our atmosphere is made up of $78\\% \\text{n}_2$, $21\\% \\text{o}_2$, and $1\\%$ other gases. what is the…

Explanation:

Step1: Identify the mole fraction of Nitrogen

The percentage of $N_{2}$ is $78%$, so the mole fraction $\chi_{N_{2}}$ is: $$\chi_{N_{2}} = \frac{78}{100} = 0.78$$

Step2: Apply Dalton's Law of Partial Pressures

The partial pressure $P_{N_{2}}$ is the product of mole fraction and total pressure $P_{total}$: $$P_{N_{2}} = \chi_{N_{2}} \times P_{total}$$

Step3: Calculate the final value

Substitute $0.78$ for $\chi_{N_{2}}$ and $0.980\text{ atm}$ for $P_{total}$: $$P_{N_{2}} = 0.78 \times 0.980\text{ atm} = 0.7644\text{ atm}$$

Answer:

$P_{N_{2}} = 0.7644\text{ atm}$