Question

Suppose that 0.95 g of water condenses on a 75.0 g block of iron that is initially at 22 °C. If the heat released during condensation goes only to warming the iron block, what is the final tempera- ture (in Celsius) of the iron block? (Assume a constant enthalpy ofvaporizationforwaterof44.0kJmol-1.)

Answer 1

The temperature of the iron block is 68.5°C.

Step-by-step explanation:

The heat released during condensation of water is used to warm the iron block:

q = m_H2O * ΔH_vap = m_fe * c_fe * ΔT

where q is the heat released, m_H2O is the mass of water condensed, ΔH_vap is the enthalpy of vaporization for water, m_fe is the mass of iron, c_fe is the specific heat capacity of iron, and ΔT is the change in temperature of the iron block.

Rearranging the equation gives:

ΔT = (m_H2O * ΔH_vap) / (m_fe * c_fe)

Substituting the given values gives:

ΔT = (0.95 g * 44.0 kJ/mol) / (75.0 g * 0.449 J/(g°C))

ΔT = 46.5°C

Therefore, the final temperature of the iron block is:

T_f = T_i + ΔT = 22°C + 46.5°C = 68.5°C.

The final temperature of the iron block is 68.5°C.