Final answer:
By equating the heat gained by the melting ice to the heat lost by the water, and using the enthalpy of fusion for ice and the specific heat of water, the calculation reveals that there were approximately 595 grams of water in the sample.
Step-by-step explanation:
To find out how many grams of water were in the sample before adding the ice, we need to equate the heat gained by the melting ice to the heat lost by the water when its temperature decreased from 7.4 °C to 0.0 °C. The enthalpy of fusion of ice, which is the amount of heat required to melt the ice without changing its temperature, is a key concept in this problem. The specific heat of water is also an important factor as it influences the amount of heat water can lose or absorb.
The enthalpy of fusion of ice is typically given as 334 J/g. Using this, the heat gained by the ice as it melts can be calculated by multiplying the mass of the ice (48 g) by the enthalpy of fusion. The heat lost by the water can be calculated using the specific heat of water (4.184 J/g°C), the change in temperature (7.4 °C), and the unknown mass of water.
Heat gained by ice = Heat lost by water (Qice = Qwater)
334 J/g × 48 g = 4.184 J/g°C × (mass of water) × 7.4 °C
By rearranging the equation, we find the mass of water:
mass of water = (334 J/g × 48 g) / (4.184 J/g°C × 7.4 °C)
After solving, the mass of the water is approximately 595 g.