Answer
$230.34$ grams of Oxygen
$115.42$ grams of Sulfur
Work Step by Step
We know that the mass of sulfur to the mass of hydrogen to the mass of oxygen is the same for any amount of a $H_2SO_4$ sample. So, we set up a table:
\begin{array}{ccc}
\text{Element}& \text{Old Amount} & \text{New Amount} \\
\text{Hydrogen}& 2.02 g & 7.27 g \\
\text{Sulfur}& 32.07 g & x \\
\text{Oxygen}& 64.00 g & y \\
\end{array}
where $x$ and $y$ are the new amounts for sulfur and oxygen, respectively. We notice that the change from the old amount of Hydrogen to the new amount of Hydrogen is $\frac{7.27}{2.02}$, as
\begin{align*}
2.02 \cdot \frac{7.27}{2.02}=7.27.
\end{align*}
So, we can use this proportion on each of the other values, and we get
\begin{align*}
\text{Oxygen: } 64.00 \cdot \frac{7.27}{2.02} \approx 230.34
\end{align*}
and
\begin{align*}
\text{Sulfur: } 32.07 \cdot \frac{7.27}{2.02} \approx 115.42
\end{align*}
So, there are approximately $230.34$ grams of Oxygen and $115.42$ grams of Sulfur in this new sample.
