Sure! Let's solve this step-by-step:
1. First, we identify the given masses of hydrogen and oxygen in the compound:
- Mass of hydrogen ([tex]\(m_{H}\)[/tex]) = 20.0 grams
- Mass of oxygen ([tex]\(m_{O}\)[/tex]) = 162.0 grams
2. We need to calculate the total mass of the compound. This is done by adding the mass of hydrogen and the mass of oxygen together:
[tex]\[
\text{Total mass} = m_H + m_O = 20.0 \, \text{grams} + 162.0 \, \text{grams} = 182.0 \, \text{grams}
\][/tex]
3. Next, we calculate the percent of oxygen in the compound by mass. The formula for the percent by mass is:
[tex]\[
\text{Percent oxygen by mass} = \left( \frac{m_O}{\text{Total mass}} \right) \times 100
\][/tex]
Plugging in the values we have:
[tex]\[
\text{Percent oxygen by mass} = \left( \frac{162.0}{182.0} \right) \times 100
\][/tex]
4. Solving this, we get:
[tex]\[
\text{Percent oxygen by mass} = 0.8901098901098901 \times 100 \approx 89.0\%
\][/tex]
Therefore, the percent oxygen by mass in the sample is approximately [tex]\(89.0\%\)[/tex].
Out of the given options, the correct answer is:
- [tex]\(89.0\%\)[/tex]
Thus, [tex]\( \boxed{89.0\%} \)[/tex] is the correct percent of oxygen by mass in the sample.
