Question

A 28.0 g sample of an unknown metal at 99°C was placed in a constant-pressure calorimeter containing 70.0 g of water at 24°C. The final temperature of the system was found to be 28.4°C. Calculate the specific heat of the metal.

Answer 1

To find the specific heat of the metal, use the conservation of energy, which equates the heat lost by the metal and the heat gained by the water. With the given masses and temperature changes, apply the heat equation q = mcΔT for both water and the metal, and solve for the metal's specific heat.

Step-by-step explanation:

To calculate the specific heat of the unknown metal, we use the principle of conservation of energy which states that the heat lost by the metal will be equal to the heat gained by the water, assuming no heat is lost to the surroundings.

The formula for heat is q = mcΔT where q is heat in joules, m is mass in grams, c is specific heat capacity in J/g°C, and ΔT is the change in temperature in °C.

For water:
qwater = mwater × cwater × ΔTwater
For the metal:
qmetal = mmetal × cmetal × ΔTmetal

Since qwater = -qmetal and cwater is known (4.18 J/g°C), we can rearrange to solve for cmetal:

cmetal = × rac{mwater × cwater × ΔTwater}{mmetal × ΔTmetal}

Using the given data:

• mwater = 70.0 g
• mmetal = 28.0 g
• ΔTwater = 28.4°C - 24°C = 4.4°C
• ΔTmetal = 99°C - 28.4°C = 70.6°C

Plugging in the values:

cmetal = × rac{(70.0 g) × (4.18 J/g°C) × (4.4°C)}{(28.0 g) × (70.6°C)}

Do the math and you'll find the specific heat capacity of the unknown metal.