A sample of liquid mercury (mass 58 g and temperature 149.0 C) is poured into 79 g of H2O at 19 C. Calculate the final temperature of the mixture, assuming no heat is lost. The heat capacities of Hg and H2O are 27.98 and 75.33 J/mol/K, respectively.

See the Au and H2O. All of the use the same concept and the same formula.

heat lost by one + heat gained by other = 0

To calculate the final temperature of the mixture, we can use the principle of conservation of energy. Since no heat is lost, the heat gained by the mercury must be equal to the heat lost by the water.

To calculate the heat gained by the mercury, we can use the formula:

q = m * c * ΔT

Where q is the heat gained, m is the mass of the substance, c is the specific heat capacity, and ΔT is the change in temperature.

For the mercury:

q_mercury = (58 g) * (27.98 J/mol/K) * (Tf - 149.0 C)

Where Tf is the final temperature.

To calculate the heat lost by the water, we use the same formula:

q_water = (79 g) * (75.33 J/mol/K) * (Tf - 19 C)

Since no heat is lost or gained, we can set the two equations equal to each other:

q_mercury = q_water

(58 g) * (27.98 J/mol/K) * (Tf - 149.0 C) = (79 g) * (75.33 J/mol/K) * (Tf - 19 C)

Simplifying the equation:

(1625.48 g * J * Tf - 97212 g * J) = (5970.07 g * J * Tf - 90407 g * J)

Rearranging the equation:

(5970.07 g * J * Tf - 1625.48 g * J * Tf) = (97212 g * J - 90407 g * J)

Combining like terms:

(4344.59 g * J * Tf) = (6790 g * J)

Dividing both sides of the equation by (4344.59 g * J):

Tf = (6790 g * J) / (4344.59 g * J)

Tf ≈ 1.561 K

Therefore, the final temperature of the mixture is approximately 1.561 K.