2.5 g of sugar is dissolved in 47.5 g of water. What is its concentration as percent by mass ?

Question

Accepted Answer

To determine the concentration of sugar as a percent by mass, we need to calculate the mass percent of sugar in the solution. The formula for percent by mass is:

$$
\text{Percent by mass} = \left( \frac{\text{mass of solute}}{\text{mass of solution}} \right) \times 100
$$

In this problem, the solute is sugar, and the solvent is water. The mass of the solute (sugar) is 2.5 g, and the mass of the solvent (water) is 47.5 g. The total mass of the solution is the sum of the mass of the solute and the mass of the solvent:

$$
\text{Mass of solution} = \text{mass of solute} + \text{mass of solvent} = 2.5 \, \text{g} + 47.5 \, \text{g} = 50.0 \, \text{g}
$$

Now, we can calculate the percent by mass of sugar in the solution:

$$
\text{Percent by mass} = \left( \frac{2.5 \, \text{g}}{50.0 \, \text{g}} \right) \times 100 = 5.00\%
$$

Thus, the concentration of sugar as a percent by mass is 5.00%, which corresponds to Option 2.

**Explanation for why each of the other options is incorrect:**

1. **Option 1 (5.26%)**: This option is incorrect because it results from a miscalculation. The correct calculation, as shown above, yields 5.00%, not 5.26%.

2. **Option 3 (19.00%)**: This option is incorrect because it significantly overestimates the concentration of sugar. The calculation clearly shows that the percent by mass is 5.00%, not 19.00%.

3. **Option 4 (50.00%)**: This option is incorrect because it suggests that the mass of sugar is equal to the mass of the entire solution, which is not the case. The mass of sugar is only 2.5 g out of a total of 50.0 g, leading to a concentration of 5.00%, not 50.00%.

In conclusion, the correct answer is Option 2, with a concentration of 5.00% by mass, as calculated using the appropriate formula and given data.