To find the rate of flour per cup of water, we start with the given ratio in the recipe: for every 2 cups of flour, there is 1/3 cup of water.
To convert this ratio into cups of flour per cup of water, we can express it as a fraction:
\[ \text{Rate} = \frac{\text{cups of flour}}{\text{cups of water}} = \frac{2 \text{ cups of flour}}{\frac{1}{3} \text{ cup of water}} \]
When dividing by a fraction, we multiply by its reciprocal:
\[ \frac{2}{\frac{1}{3}} = 2 \times 3 = 6 \]
So, the rate is 6 cups of flour for every 1 cup of water.
Therefore, Sophie uses 6 cups of flour per cup of water.