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**Problem**: Under constant pressure conditions, a 107 g block of metal at 125°C is added to a mixture of 120 g of water and 22 g of ice at 0°C. As a result, the ice melts completely and the temperature of the water increases to 7°C.Given that the specific heat capacity of water is 4.184 J/g·K and its enthalpy of fusion is 6.01 kJ/mol, calculate the specific heat capacity (in J/g·K) of the metal. Show all work and circle your final answer.

###### FREE Expert Solution

We’re being asked to determine the specific heat capacity of the metal.

We will use the heat released by the metal piece to calculate its heat capacity. Recall that heat can be calculated using the following equation:

$\overline{){\mathbf{q}}{\mathbf{=}}{\mathbf{mc}}{\mathbf{\u2206}}{\mathbf{T}}}$

q = heat, J

• **+q** → **absorbs **heat

• **–q** → **l****oses **heat

m = mass (g)

c = specific heat capacity = J/(g·°C)

ΔT = T_{f} – T_{i} = (°C)

The heat absorbed when melting ice at it's melting point can be represented by the equation below:

$\overline{){\mathbf{q}}{\mathbf{}}{\mathbf{=}}{\mathbf{n}}{\mathbf{\u2206}}{{\mathbf{H}}}_{{\mathbf{fus}}}}$

n = moles

ΔH_{fus} = heat of fusion

**Based on the given system:**

###### Problem Details

Under constant pressure conditions, a 107 g block of metal at 125°C is added to a mixture of 120 g of water and 22 g of ice at 0°C. As a result, the ice melts completely and the temperature of the water increases to 7°C.

Given that the specific heat capacity of water is 4.184 J/g·K and its enthalpy of fusion is 6.01 kJ/mol, calculate the specific heat capacity (in J/g·K) of the metal. Show all work and circle your final answer.

Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Constant-Pressure Calorimetry concept. You can view video lessons to learn Constant-Pressure Calorimetry Or if you need more Constant-Pressure Calorimetry practice, you can also practice Constant-Pressure Calorimetry practice problems .