Final answer:
The mass of the water sample is approximately 277.2 grams.
Step-by-step explanation:
To determine the mass of the water sample, we can use the formula q = m * c * ΔT, where q is the heat added to the water, m is the mass of the water, c is the specific heat of water, and ΔT is the change in temperature. Rearranging the formula, we have m = q / (c * ΔT). Plugging in the given values, we get m = 27.6 kJ / (4.184 J/g•K * (65.7 °C - 22.3 °C)). Solving this equation, we find that the mass of the water sample is approximately 277.2 grams.