Question

How many molecules of sugar are there in 1 can of soda?

Answer 1

Answer:

$5.8\cdot 10^{22}$

Explanation:

Since no information was provided about the can of soda, let's take an example of 1 can of 12 fl oz (368 g) Coca-Cola.

The nutrition facts state that it contains 33 g of sugar. In order to calculate the number of molecules, we firstly need to know the molecular formula of sugar. Sugar can be represented by $C_{12}H_{22}O_{11}$.

Our first step is to find the molar mass of sugar:

$M_{C_{12}H_{22}O_{11}} = 342.3 g/mol$

Secondly, dividing mass of sugar, $m = 33 g$, by the molar mass will yield the number of moles of sugar:

$n_{C_{12}H_{22}O_{11}}=\frac{m}{M}$

Finally, multiplying moles by the Avogadro's constant will yield the number of molecules:

$N_{C_{12}H_{22}O_{11}}=n_{C_{12}H_{22}O_{11}}\cdot N_A =\frac{m}{M} \cdot N_A = \frac{33 g}{342.3 g/mol} \cdot 6.022 \cdot 10^{23} mol^{-1} = 5.8\cdot 10^{22}$