Question 1 (2 points) \begin{tabular}{|l|l|}\hline\( \equiv \) & Listen \\ How many kg of O are contained in \( 2.86 \times 10^{25} \) molecules of \( \mathrm{Mg}_{(}\left(\mathrm{ClO}_{4}\right) 2 \) \\ (Answer to 2 decimal place) \\ Your Answer: \end{tabular}

To find out how many kilograms of oxygen (O) are contained in \( 2.86 \times 10^{25} \) molecules of \( \mathrm{Mg(ClO_4)_{2}} \), we can follow these steps: 1. **Determine the number of oxygen atoms in one molecule of \( \mathrm{Mg(ClO_4)_{2}} \)**: - Each \( \mathrm{ClO_4} \) contains 4 oxygen atoms. - Since there are 2 \( \mathrm{ClO_4} \) groups in \( \mathrm{Mg(ClO_4)_{2}} \), the total number of oxygen atoms in one molecule is: \[ 2 \times 4 = 8 \text{ oxygen atoms} \] 2. **Calculate the total number of oxygen atoms in \( 2.86 \times 10^{25} \) molecules**: \[ \text{Total oxygen atoms} = 2.86 \times 10^{25} \text{ molecules} \times 8 \text{ oxygen atoms/molecule} = 2.288 \times 10^{26} \text{ oxygen atoms} \] 3. **Convert the number of oxygen atoms to moles**: - Use Avogadro's number, \( 6.022 \times 10^{23} \) atoms/mole: \[ \text{Moles of oxygen} = \frac{2.288 \times 10^{26} \text{ oxygen atoms}}{6.022 \times 10^{23} \text{ atoms/mole}} \approx 379.5 \text{ moles of O} \] 4. **Calculate the mass of oxygen**: - The molar mass of oxygen (O) is approximately \( 16.00 \, \text{g/mol} \): \[ \text{Mass of oxygen} = 379.5 \text{ moles} \times 16.00 \, \text{g/mol} = 6072 \text{ g} \] 5. **Convert grams to kilograms**: \[ \text{Mass in kg} = \frac{6072 \text{ g}}{1000} = 6.072 \text{ kg} \] 6. **Round to two decimal places**: \[ \text{Final answer} = 6.07 \text{ kg} \] Your Answer: **6.07 kg**