Question

How many molecules are contained in 4.00g of CO2 if the Molar mass of CO2 is 44.00 g/mole?

Answer 1

`\boxed {\boxed {\sf 5.47 * 10^(22) \ molecules \ CO_2}}`

Step-by-step explanation:

We are asked to find how many molecules are contained in 4.00 grams of carbon dioxide.

1. Grams to Moles

Convert grams to moles using the molar mass (mass of 1 mole of a substance). The molar mass of carbon dioxide is given: 44.00 grams per mole.

We will convert using dimensional analysis. Set up a conversion factor using the molar mass.

`\frac {44.0 \ g \ CO_2}{ 1 \ mol \ CO_2}`

We are converting 4.00 grams of carbon dioxide to moles, so we multiply by this value.

`4.00 \ g \ CO_2 * \frac {44.0 \ g \ CO_2}{ 1 \ mol \ CO_2}`

Flip the conversion factor. The value remains the same, but it allows us to cancel the units of grams of carbon dioxide.

`4.00 \ g \ CO_2 * \frac { 1 \ mol \ CO_2}{44.0 \ g \ CO_2}`

`4.00 * \frac { 1 \ mol \ CO_2}{44.0 }`

`\frac {4.00}{44.00 } \ mol \ CO_2`

`0.09090909091 \ mol \ CO_2`

2. Moles to Molecules

Convert moles to molecules using Avogadro's Number or 6.022 × 10²³. This is the number of particles (atoms, molecules, formula units, etc.) in 1 mole of a substance. In this case, the particles are molecules of carbon dioxide.

Set up another conversion factor, this time with Avogadro's Number.

`\frac {6.022 * 10^(23) \ molecules \ CO_2}{ 1\ mol \ CO_2}`

We are converting 0.09090909091 moles of carbon dioxide to molecules, so we multiply by this value.

`0.09090909091 \ mol \ CO_2*\frac {6.022 * 10^(23) \ molecules \ CO_2}{ 1\ mol \ CO_2}`

The units of moles of carbon dioxide cancel.

`0.09090909091 *\frac {6.022 * 10^(23) \ molecules \ CO_2}{ 1}`

`0.09090909091 *{6.022 * 10^(23) \ molecules \ CO_2}`

`5.47454545 * 10^(22)} \ molecules \ CO_2`

3. Significant Figures

The measurement of molar mass (44.00) has 4 sig fig and the measurement of molecules (4.00) has 3 sig fig. We round to the least number of sig fig, or 3.

For the number we found, that is the hundredth place. The 4 in the thousandth place tells us to leave the 7.

`5.47 * 10^(22) \ molecules \ CO_2`

4.00 grams of carbon dioxide contains 5.47 × 10²² molecules of carbon dioxide.

Answer 2

5.47 × 10²² CO₂ molecules

Step-by-step explanation:

We want to determine the amount of molecules of CO₂ in 4.00 grams of CO₂ given that its molar mass is 44.00 g/mol.

To convert from grams to molecules, we can first convert from grams to moles and then from moles to molecules using the following two ratios:

`\displaystyle \frac{1 \text{ mol CO$_2$}}{44.00 \text{ g CO$_2$}}\text{ and } \frac{6.02 \cdot 10^(23) \text{ molecules CO$_2$}}{1 \text{ mol CO$_2$}}`

Begin with the initial value and multiply:

`\displaystyle \begin{aligned} &4.00 \text{ g CO$_2$} \cdot \frac{1 \text{ mol CO$_2$}}{44.00 \text{ g CO$_2$}}\cdot \frac{6.02 * 10^(23) \text{ molecules CO$_2$}}{1 \text{ mol CO$_2$}} \\ \\ &= 5.47 * 10^(22) \text{ molecules CO$_2$}}\end{aligned}`

Note that the final result should have three significant digits since 4.00 has three sig. digs.

In conclusion, there are about 5.47 × 10²² CO₂ molecules in 4.00 grams of CO₂.