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How much heat is released when 25.0 grams of liquid copper at its freezing point of [tex]$1,085^{\circ} C[tex]$[/tex] changes to solid? The latent heat of fusion of copper is [tex]$[/tex]205.0 \, \text{J/g}$[/tex].

A. [tex]-27,130 \, \text{J}[/tex]
B. [tex]-5,130 \, \text{J}[/tex]
C. [tex]5,130 \, \text{J}[/tex]
D. [tex]27,130 \, \text{J}[/tex]



Answer :

GinnyAnswer
To determine how much heat is released when 25.0 grams of liquid copper at its freezing point of \(1,085^{\circ} C\) changes to solid, we use the concept of latent heat of fusion. The latent heat of fusion (or enthalpy of fusion) is the amount of heat energy required to change 1 gram of a substance from solid to liquid (or liquid to solid) at its melting/freezing point without a change in temperature.

Given:
- Mass of copper, \( m = 25.0 \) grams
- Latent heat of fusion of copper, \( L = 205.0 \, \text{J/g} \)

The heat \( Q \) released during the phase change can be calculated using the formula:
[tex]\[ Q = m \times L \][/tex]

Substituting in the given values:
[tex]\[ Q = 25.0 \, \text{g} \times 205.0 \, \text{J/g} \][/tex]

Let's proceed with the multiplication:
[tex]\[ Q = 5125.0 \, \text{J} \][/tex]

Since the copper is releasing heat as it changes from the liquid to solid phase, the heat released is negative:
[tex]\[ Q = -5125.0 \, \text{J} \][/tex]

Therefore, the amount of heat released is \( -5125.0 \, \text{J} \).

Comparing this result to the provided choices:
- \( -27,130 \, \text{J} \)
- \( -5,130 \, \text{J} \) (This appears to be a minor typographical error and should be \( -5,125.0 \, \text{J} \))
- \( 5,130 \, \text{J} \)
- \( 27,130 \, \text{J} \)

The correct answer is:
[tex]\[ -5,130 \, \text{J} \][/tex]

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