Answer :
To understand how stoichiometry is used to calculate the energy absorbed when a mass of solid melts, we need to consider the process of melting and the heat involved in this phase change. The key to this calculation is the concept of the heat of fusion (∆H_fusion), which is the amount of energy required to change a substance from the solid phase to the liquid phase at its melting point.
Here's a detailed step-by-step explanation of the process:
1. Identify the Given Mass and the Substances' Molar Mass:
We start with a given mass of the solid substance in grams. For the purposes of the calculation, it's useful to know the molar mass (g/mol) of the substance, but this is not provided explicitly in the options or the problem.
2. Convert Grams to Moles:
To use the heat of fusion, which is typically expressed in terms of energy per mole (kJ/mol), we need to convert the mass of the solid from grams to moles. This is done using the molar mass of the substance:
[tex]\[ \text{moles} = \frac{\text{grams of solid}}{\text{molar mass in g/mol}} \][/tex]
This step essentially gives us the quantity of the substance in molar terms, which is crucial because ∆H_fusion is given per mole.
3. Multiply by Heat of Fusion:
Once we have the number of moles, we multiply this by the heat of fusion (∆H_fusion). The heat of fusion is a specific value for each substance and represents the amount of energy (usually in kJ) required to melt one mole of the substance at its melting point.
[tex]\[ \text{energy absorbed} = \text{moles of solid} \times \Delta H_{\text{fusion}} \][/tex]
Here, ∆H_fusion directly relates the amount of energy absorbed to the number of moles of solid.
Putting this together, the formula to calculate the energy absorbed when a mass of solid melts is:
[tex]\[ \text{energy absorbed} = \text{grams solid} \times \left(\frac{1 \text{ mol}}{\text{grams solid}}\right) \times \Delta H_{\text{fusion}} \][/tex]
After ensuring the unit conversions and considering the context of the melting process, it becomes clear that the correct expression for calculating the energy absorbed is:
[tex]\[ \text{Grams solid} \times \left(\frac{1 \text{ mol}}{\text{grams solid}}\right) \times \Delta H_{\text{fusion}} \][/tex]
Thus, the correct answer is:
A. Grams solid [tex]$\times \frac{\text{mol}}{\text{g}} \times \Delta H_{\text{fusion}}$[/tex]
Here's a detailed step-by-step explanation of the process:
1. Identify the Given Mass and the Substances' Molar Mass:
We start with a given mass of the solid substance in grams. For the purposes of the calculation, it's useful to know the molar mass (g/mol) of the substance, but this is not provided explicitly in the options or the problem.
2. Convert Grams to Moles:
To use the heat of fusion, which is typically expressed in terms of energy per mole (kJ/mol), we need to convert the mass of the solid from grams to moles. This is done using the molar mass of the substance:
[tex]\[ \text{moles} = \frac{\text{grams of solid}}{\text{molar mass in g/mol}} \][/tex]
This step essentially gives us the quantity of the substance in molar terms, which is crucial because ∆H_fusion is given per mole.
3. Multiply by Heat of Fusion:
Once we have the number of moles, we multiply this by the heat of fusion (∆H_fusion). The heat of fusion is a specific value for each substance and represents the amount of energy (usually in kJ) required to melt one mole of the substance at its melting point.
[tex]\[ \text{energy absorbed} = \text{moles of solid} \times \Delta H_{\text{fusion}} \][/tex]
Here, ∆H_fusion directly relates the amount of energy absorbed to the number of moles of solid.
Putting this together, the formula to calculate the energy absorbed when a mass of solid melts is:
[tex]\[ \text{energy absorbed} = \text{grams solid} \times \left(\frac{1 \text{ mol}}{\text{grams solid}}\right) \times \Delta H_{\text{fusion}} \][/tex]
After ensuring the unit conversions and considering the context of the melting process, it becomes clear that the correct expression for calculating the energy absorbed is:
[tex]\[ \text{Grams solid} \times \left(\frac{1 \text{ mol}}{\text{grams solid}}\right) \times \Delta H_{\text{fusion}} \][/tex]
Thus, the correct answer is:
A. Grams solid [tex]$\times \frac{\text{mol}}{\text{g}} \times \Delta H_{\text{fusion}}$[/tex]
