# Question 500f0

Feb 2, 2017

$\text{166.520 torr}$

#### Explanation:

The first thing to do is to convert the total pressure of the mixture from atmospheres to torr by using the conversion factor

$\textcolor{b l u e}{\underline{\textcolor{b l a c k}{\text{1 atm " = " 760 torr}}}}$

As you can see, the total pressure of the mixture will be equal to

${P}_{\text{total" = "760 torr}}$

Now, Dalton's Law of Partial Pressures states that the total pressure of a gas mixture is equal to the sum of the individual partial pressures of the gases that make up the mixture.

In other words, the partial pressures of the three gases must amount to the total pressure of the mixture.

P_"total" = P_ ("CO"_ 2) + P_ ("N"_ 2) + P_( "O"_ 2)

You can thus say that the aprtial pressure of oxygen gas will be equal to

P_( "O"_ 2) = P_"total" - (P_ ("CO"_ 2) + P_ ("N"_ 2))

In your case, you will have

P_ ("CO"_ 2) + P_ ("N"_ 2) = "593.425 torr" + "0.055 torr" = "593.480 torr"

Keep in mind that the value must be rounded to three decimal places.

The partial pressure of oxygengas will thus be

color(darkgreen)(ul(color(black)(P_ ("O"_ 2) = "760 torr" - "593.480 torr" = "166.520 torr")))

The answer must also be rounded to three decimal places because $\text{760 torr}$ is a constant, meaning that we defined $\text{1 atm}$ to be equal to $\text{760 torr}$.

Thsi implies that you can use as many decimal palces with this value as you have for your actual data.

In other words, you have

color(darkgreen)(ul(color(black)(P_ ("O"_ 2) = "760.000 torr" - "593.480 torr" = "166.520 torr")))#

We can use $\text{760.000 torr}$ because the value we're subtracting is rounded to three decimal places.

Finally, keep in mind that when working with addition or subtraction, like we are doing here, the number of significant figures is always given by the number of value with the least number of decimal places.

• $\text{593.425 torr } \to$ six sig figs, three decimal places
• $\text{0.055 torr } \to$ two sig figs, three decimal places

This is why the answer must be rounded to three decimal places, not to two significant figures.