Question

You exhale about .0800 liters of CO2 (carbon dioxide) gas in a single breath. 22.4 liters of CO2 contain 6.022 x 1023 molecules. 6,022 x 1023 CO2 molecules have a mass of 44.0 grams. Find the A) number of carbon dioxide molecules you exhale in each breath. Find the mass of the CO2 you exhale in a single breath.

Answer 1

Answer:

A) $2.150 * 10^{22}$

B) 1.57 grams

Explanation:

Given -

Amount of gas exhaled in one single breathe $= 0.080$ liters

$22.4$ liter of carbon dioxide contains $6.022 * 10^{23}$ molecules

One liter of carbon dioxide contains $= \frac{6.022*10^{23}}{22.4}\\= 2.688 * 10^{23}$

A) Number of molecules in $0.08$ liter of carbon dioxide $= 0.08 * 2.688 * 10^{23}\\= 2.150 * 10^{22}$

B) Mass of $6.022 * 10^{23}$ molecules is equal to $44$ grams

Mass of one molecule $= \frac{44}{6.022*10^{23}} \\= 7.306*10^{-23}$

Mass of molecule is$[tex]7.306*10^{-23} * 2.150 * 10^{22}\\= 1.57$[/tex]  gram

Answer 2

Taking into account the rule of three:

• the number of carbon dioxide molecules you exhale in each breath is 2.15×10²¹.
• the mass of the CO₂ you exhale in a single breath is 0.157 grams.

Rule of three

In first place, the rule of three is a way of solving problems of proportionality between three known values and an unknown value, establishing a relationship of proportionality between all of them.

That is, what is intended with it is to find the fourth term of a proportion knowing the other three.  

If the relationship between the magnitudes is direct, that is, when one magnitude increases, so does the other (or when one magnitude decreases, so does the other) , the direct rule of three must be applied.

To solve a direct rule of three, the following formula must be followed, being a, b and c known data and x the variable to be calculated:

a ⇒ b

c ⇒ x

So: $x=\frac{cxb}{a}$

Number of carbon dioxide molecules

To find the number of carbon dioxide molecules, you know that 22.4 liters of CO₂ contain 6.022×10²³ molecules.

If you exhale about 0.0800 liters of CO₂ (carbon dioxide) gas in a single breath, you can aply the following rule of three: if 22.4 liters of CO₂ contain 6.022×10²³ molecules, 0.0800 liters contain how many molecules?

$amount of molecules=\frac{0.0800 litersx6.022x10^{23} molecules}{22.4 liters}$

amount of molecules= 2.15×10²¹

Finally, the number of carbon dioxide molecules you exhale in each breath is 2.15×10²¹.

Mass of the CO₂ you exhale in a single breath

To find the mass of the CO₂, you know that 6.022×10²³ molecules have a mass of 44.0 grams.

If you exhale about 2.15×10²¹ molecules of CO₂ (carbon dioxide) gas in a single breath, you can aply the following rule of three: if 6.022×10²³ molecules have a mass of 44.0 grams, 2.15×10²¹ molecules contain how much mass?

$mass=\frac{2.15x10^{21}moleculesx44 grams }{6.022x10^{23} molecules}$

mass= 0.157 grams

Finally, the mass of the CO₂ you exhale in a single breath is 0.157 grams.

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