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How much energy is required to vaporize [tex]$2 \, \text{kg}$[/tex] of aluminum? Use the table below and this equation: [tex]$Q = mL_{\text{vapor}}$[/tex].

\begin{tabular}{|c|c|c|c|c|}
\hline
Substance & \begin{tabular}{c}
Latent Heat \\
Fusion \\
(melting) \\
(kJ/kg)
\end{tabular} & \begin{tabular}{c}
Melting \\
Point \\
[tex]$\left(^{\circ}C \right)$[/tex]
\end{tabular} & \begin{tabular}{c}
Latent Heat \\
Vaporization \\
(boiling) [tex]$( kJ / kg )$[/tex]
\end{tabular} & \begin{tabular}{c}
Boiling \\
Point \\
[tex]$\left(^{\circ}C \right)$[/tex]
\end{tabular} \\
\hline
Aluminum & 400 & 660 & 1100 & 2450 \\
\hline
Copper & 207 & 1083 & 4730 & 2566 \\
\hline
Gold & 62.8 & 1063 & 1720 & 2808 \\
\hline
Helium & 5.2 & -270 & 21 & -269 \\
\hline
Lead & 24.5 & 327 & 871 & 1751 \\
\hline
Mercury & 11.4 & -39 & 296 & 357 \\
\hline
Water & 335 & 0 & 2256 & 100 \\
\hline
\end{tabular}

A. [tex]$4520 \, \text{kJ}$[/tex]

B. [tex]$1794 \, \text{kJ}$[/tex]

C. [tex]$800 \, \text{kJ}$[/tex]

D. [tex]$2200 \, \text{kJ}$[/tex]


Sagot :

To find the amount of energy required to vaporize 2 kg of aluminum, we can use the equation \( Q = m L_{\text {vapor}} \), where:
- \( Q \) is the energy required,
- \( m \) is the mass,
- \( L_{\text {vapor}} \) is the latent heat of vaporization.

From the provided table, we can find that the latent heat of vaporization for aluminum is \( 1100 \, \text{kJ/kg} \).

Given:
- Mass of aluminum, \( m = 2 \, \text{kg} \),
- Latent heat of vaporization of aluminum, \( L_{\text {vapor}} = 1100 \, \text{kJ/kg} \).

Substituting these values into the equation \( Q = m L_{\text {vapor}} \):

[tex]\[ Q = 2 \, \text{kg} \times 1100 \, \text{kJ/kg} \][/tex]

[tex]\[ Q = 2200 \, \text{kJ} \][/tex]

Therefore, the amount of energy required to vaporize 2 kg of aluminum is \( 2200 \, \text{kJ} \).

The correct answer is:
D. [tex]\( 2200 \, \text{kJ} \)[/tex]
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