A 13.8 g piece of Zn metal was heated to 98.6 oC and then dropped in 45.6 g of water at 25.0 oC. Assuming that no heat is lost to the surroundings, determine the specific heat capacity of Zn if the final temperature of the water was 27.1 oC C=6461.39

heat lost by Zn + heat gained by water = 0

[mass Zn x specific heat Zn x (Tfinal-Tinitial)] + [mass H2O x specific heat H2O x (Tfinal-Tinitial)] = 0

Substitute and solve for the one unknown.

To determine the specific heat capacity of Zn, we can use the principle of heat transfer:

Q₁ + Q₂ = 0

Where Q₁ is the heat gained by the water, and Q₂ is the heat lost by the zinc.

First, let's calculate the heat gained by the water (Q₁). We can use the equation:

Q = mcΔT

Where Q is the heat gained or lost, m is the mass of the water, c is the specific heat capacity of water, and ΔT is the change in temperature of the water.

Given:
m₁ = 45.6 g (mass of water)
c₁ = 4.18 J/g°C (specific heat capacity of water)
ΔT₁ = 27.1°C - 25.0°C = 2.1°C (change in temperature of water)

Plugging in the values, we have:

Q₁ = (45.6 g) * (4.18 J/g°C) * (2.1°C)
Q₁ = 400.3784 J

Next, let's calculate the heat lost by zinc (Q₂). We can use the equation:

Q₂ = mcΔT

Where Q₂ is the heat lost by the zinc, m is the mass of the zinc, c is the specific heat capacity of zinc, and ΔT is the change in temperature of the zinc.

Given:
m₂ = 13.8 g (mass of zinc)
c₂ = ? (specific heat capacity of zinc)
ΔT₂ = 98.6°C - 27.1°C = 71.5°C (change in temperature of zinc)

Since we want to find c₂, we rearrange the formula:

c₂ = Q₂ / (m₂ * ΔT₂)

Substituting the values, we have:

c₂ = 400.3784 J / (13.8 g * 71.5°C)
c₂ = 0.413 J/g°C

As such, the specific heat capacity of Zn is approximately 0.413 J/g°C.