Question

convert $1.20 \times 10^{24}$ molecules of $\ce{h_2o}$ to moles. show your work.

Explanation:

Step1: Recall Avogadro's Number

Avogadro's number is \( 6.022 \times 10^{23} \) molecules per mole. The formula to convert molecules to moles is \( \text{Moles} = \frac{\text{Number of Molecules}}{\text{Avogadro's Number}} \).

Step2: Substitute the Values

We have \( 1.20 \times 10^{24} \) molecules of \( \text{H}_2\text{O} \) and Avogadro's number \( 6.022 \times 10^{23} \) molecules/mol. Plugging into the formula: \( \text{Moles} = \frac{1.20 \times 10^{24}}{6.022 \times 10^{23}} \).

Step3: Perform the Calculation

Simplify the expression: \( \frac{1.20 \times 10^{24}}{6.022 \times 10^{23}}=\frac{1.20}{6.022}\times10^{24 - 23}\approx0.1993\times 10^{1}\approx1.99\) (or approximately 2.00 when using \( 6.02\times 10^{23} \) for simplicity).

Answer:

Approximately \( 1.99 \) moles (or \( 2.00 \) moles if using \( 6.02\times 10^{23} \))