Answer:
5.47 × 10²² CO₂ molecules
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:
[tex]\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$_2$}}[/tex]
Begin with the initial value and multiply:
[tex]\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 \times 10^{23} \text{ molecules CO$_2$}}{1 \text{ mol CO$_2$}} \\ \\ &= 5.47 \times 10^{22} \text{ molecules CO$_2$}}\end{aligned}[/tex]
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.
Answer:
[tex]\boxed {\boxed {\sf 5.47 \times 10^{22} \ molecules \ CO_2}}[/tex]
Explanation:
We are asked to find how many molecules are contained in 4.00 grams of carbon dioxide.
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.
[tex]\frac {44.0 \ g \ CO_2}{ 1 \ mol \ CO_2}[/tex]
We are converting 4.00 grams of carbon dioxide to moles, so we multiply by this value.
[tex]4.00 \ g \ CO_2 * \frac {44.0 \ g \ CO_2}{ 1 \ mol \ CO_2}[/tex]
Flip the conversion factor. The value remains the same, but it allows us to cancel the units of grams of carbon dioxide.
[tex]4.00 \ g \ CO_2 * \frac { 1 \ mol \ CO_2}{44.0 \ g \ CO_2}[/tex]
[tex]4.00 * \frac { 1 \ mol \ CO_2}{44.0 }[/tex]
[tex]\frac {4.00}{44.00 } \ mol \ CO_2[/tex]
[tex]0.09090909091 \ mol \ CO_2[/tex]
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.
[tex]\frac {6.022 \times 10^{23} \ molecules \ CO_2}{ 1\ mol \ CO_2}[/tex]
We are converting 0.09090909091 moles of carbon dioxide to molecules, so we multiply by this value.
[tex]0.09090909091 \ mol \ CO_2*\frac {6.022 \times 10^{23} \ molecules \ CO_2}{ 1\ mol \ CO_2}[/tex]
The units of moles of carbon dioxide cancel.
[tex]0.09090909091 *\frac {6.022 \times 10^{23} \ molecules \ CO_2}{ 1}[/tex]
[tex]0.09090909091 *{6.022 \times 10^{23} \ molecules \ CO_2}[/tex]
[tex]5.47454545 \times 10^{22}} \ molecules \ CO_2[/tex]
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.
[tex]5.47 \times 10^{22} \ molecules \ CO_2[/tex]
4.00 grams of carbon dioxide contains 5.47 × 10²² molecules of carbon dioxide.
