A student conducts a calorimetry experiment to heat a sample of liquid water. A stream of gaseous \(\text{H}_2\text{O}\) (steam) at \(100.0\ ^\circ\text{C}\) is bubbled into an insulated flask containing \(60.0\text{ g}\) of liquid water at \(20.0\ ^\circ\text{C}\). The steam completely condenses and mixes with the liquid water until the entire system reaches a uniform final temperature of \(40.0\ ^\circ\text{C}\).

Assume no heat is lost to the calorimeter or the surroundings.

• Specific heat capacity of liquid water: \(4.18\text{ J}/(\text{g}\cdot^\circ\text{C})\)
• Enthalpy of vaporization of water: \(\Delta H_{\text{vap}} = 2.26 \times 10^3\text{ J/g}\)

What is the minimum mass of steam at \(100.0\ ^\circ\text{C}\) required to reach the final temperature of \(40.0\ ^\circ\text{C}\)?