Answer:
2.690 x 10⁻²¹ g of glucose (C6H12O6).
Explanation:
We want to find the mass in grams of 9 molecules of glucose, so we have to use Avogadro's number, which is 6.022 x 10²³ molecules/mol. This number is telling us that there are 6.022 x 10²³ molecules or units in 1 mol of any substance.
We can state a rule of three to do this. If 1 mol contains 6.022 x 10²³ molecules, how many moles will contain 9 molecules?
As we have 9 molecules of glucose (C6H12O6), the conversion from molecules to moles will look like this:
[tex]9\text{ molecules glucose}\cdot\frac{1\text{ mol glucose}}{6.022\cdot10^{23}\text{ molecules glucose}}.[/tex]
Now, let's calculate the molar mass of C6H12O6 using the periodic table. You can see that the molar mass of C is 12 g/mol, the molar mass of H is 1 g/mol and the molar mass of O is 16 g/mol. We have six C, twelve H, and six O, so we have to do an algebraic sum to find the molar mass of C6H12O6, as follows:
[tex]\begin{gathered} Mola\text{r mass of C}_6H_{12}O_6=6\cdot12\frac{g}{mol}+12\cdot1\frac{g}{mol}+6\cdot16\frac{g}{mol}, \\ \\ Mola\text{r mass of C}_6H_{12}O_6=72\frac{g}{mol}+12\frac{g}{mol}+96\frac{g}{mol}, \\ \\ Mola\text{r mass of C}_6H_{12}O_6=180\frac{g}{mol}. \end{gathered}[/tex]
So the molar mass of glucose (C6H12O6) is 180 g/mol. This is telling us that we have 180 g of glucose in 1 mol of glucose.
We can state a rule of three again to find the mass of glucose. Previously we found that we have 9/6.022 x 10²³ moles of glucose in 9 molecules of glucose and we want to find how many grams are in 9/6.022 x 10²³ moles of glucose:
So the calculation and its answer will look like this:
[tex]\frac{9\text{ moles glucose}}{6.022\cdot10^{23}}\cdot\frac{180\text{ g glucose}}{1\text{ mol glucose}}=2.690\cdot10^{-21}\text{ g glucose.}[/tex]
The answer would be that we have 2.690 x 10⁻²¹ g of glucose (C6H12O6) in 9 molecules of glucose.
