Questions: Calculate the amount of heat needed to melt 176 g of ice (H2O) and bring it to a temperature of 90.4°C. Be sure your answer has a unit symbol and the correct number of significant digits.

Solution Steps

The heat required to melt ice is given by the formula: \[ q = m \cdot \Delta H_f \] where:

• \( m \) is the mass of the ice
• \( \Delta H_f \) is the heat of fusion for ice, which is \( 334 \, \text{J/g} \)

Given: \[ m = 176 \, \text{g} \] \[ \Delta H_f = 334 \, \text{J/g} \]

So, \[ q_1 = 176 \, \text{g} \times 334 \, \text{J/g} = 58864 \, \text{J} \]

The heat required to raise the temperature of water is given by the formula: \[ q = m \cdot c \cdot \Delta T \] where:

• \( m \) is the mass of the water (same as the mass of the ice)
• \( c \) is the specific heat capacity of water, which is \( 4.184 \, \text{J/g} \cdot \text{°C} \)
• \( \Delta T \) is the change in temperature

Given: \[ m = 176 \, \text{g} \] \[ c = 4.184 \, \text{J/g} \cdot \text{°C} \] \[ \Delta T = 90.4 \, \text{°C} - 0 \, \text{°C} = 90.4 \, \text{°C} \]

So, \[ q_2 = 176 \, \text{g} \times 4.184 \, \text{J/g} \cdot \text{°C} \times 90.4 \, \text{°C} = 66610.5 \, \text{J} \]

The total heat required is the sum of the heat needed to melt the ice and the heat needed to raise the temperature of the water: \[ q_{\text{total}} = q_1 + q_2 \]

So, \[ q_{\text{total}} = 58864 \, \text{J} + 66610.5 \, \text{J} = 125474.5 \, \text{J} \]

Final Answer