Question

Calculate the amount of heat needed to melt solid ethanol and bring it to a temperature of ___. Round your answer to significant digits. Also, be sure your answer contains a unit symbol.

Answer 1

The amount of heat needed to melt 10.5 g of solid ethanol (CH₃CH₂OH) and bring it to a temperature of 59.4 °C is approximately 5.499 kJ. This calculation accounts for both the heat required to raise the temperature to 0 °C and the subsequent melting and temperature increase.

Step-by-step explanation:

To determine the heat required, we can break down the process into two steps: first, the heat needed to raise the temperature of ethanol from its melting point to 0 °C, and second, the heat needed to melt the solid ethanol and further raise its temperature to 59.4 °C.

1: Calculating the heat to raise the temperature to 0 °C

The specific heat of solid ethanol
`(\(C_{\text{solid}}\))` is approximately 2.44 J/g°C. The melting point of ethanol
`(\(T_{\text{melting}}\))` is 0 °C.

`\[ q_1 = m * C_{\text{solid}} * \Delta T_1 \]`

`\[ q_1 = 10.5 \, \text{g} * 2.44 \, \text{J/g°C} * (0 - (-114.3 \, \text{°C})) \]`

`\[ q_1 = 10.5 \, \text{g} * 2.44 \, \text{J/g°C} * 114.3 \, \text{°C} \]`

`\[ q_1 = 2,776.14 \, \text{J} \]`

2: Calculating the heat to melt the solid ethanol and raise the temperature to 59.4 °C

The heat of fusion for ethanol
`(\(\Delta H_{\text{fusion}}\))` is approximately 106 J/g, and the specific heat of liquid ethanol
`(\(C_{\text{liquid}}\))` is about 2.44 J/g°C.

`\[ q_2 = \Delta H_{\text{fusion}} + m * C_{\text{liquid}} * \Delta T_2 \]`

`\[ q_2 = 106 \, \text{J/g} + 10.5 \, \text{g} * 2.44 \, \text{J/g°C} * (59.4 \, \text{°C} - 0) \]`

`\[ q_2 = 106 \, \text{J/g} + 10.5 \, \text{g} * 2.44 \, \text{J/g°C} * 59.4 \, \text{°C} \]`

`\[ q_2 = 106 \, \text{J/g} + 2,722.68 \, \text{J} \]`

Total Heat Required:

Adding
`\(q_1\) and \(q_2\)` gives the total heat required:

`\[ \text{Total Heat} = q_1 + q_2 \]`

`\[ \text{Total Heat} = 2,776.14 \, \text{J} + 2,722.68 \, \text{J} \]`

`\[ \text{Total Heat} = 5,498.82 \, \text{J} \]`

Converting this to kilojoules (kJ):

`\[ \text{Total Heat} = 5,498.82 \, \text{J} * \frac{1 \, \text{kJ}}{1,000 \, \text{J}} \]`

`\[ \text{Total Heat} \approx 5.499 \, \text{kJ} \]`

Therefore, the amount of heat needed to melt 10.5 g of solid ethanol and raise it to a temperature of 59.4 °C is approximately 5.499 kJ, rounded to three significant digits.

Complete Question:

Calculate the amount of heat needed to melt 10.5 g of solid ethanol (CH3CH2OH) and bring it to a temperature of 59.4 C. Round your answer to 3 significant digits. Also, be sure your answer contains a unit symbol.