How many grams of C4H10O can be melted by 2.0 x 103 J?
Given ÄHfus = 7.27 kJ/mol
q = mass x heat fusion
Can you show me how to set it up. I am having a problem seting it up. Is 7.27 the mass? and then do I mutiple 2.0 x 103? I am confused. Please help. Thank you.
To determine the number of grams of C4H10O that can be melted by 2.0 x 10^3 J, we need to convert the energy into kilojoules and then use the enthalpy of fusion (ÄHfus) to calculate the amount of substance.
1. Convert the given energy from joules to kilojoules:
2.0 x 10^3 J = 2.0 x 10^3 / 1000 = 2.0 kJ
2. Divide the energy (in kilojoules) by the enthalpy of fusion (ÄHfus):
2.0 kJ / 7.27 kJ/mol = 0.2756 mol
3. Now we need to convert moles into grams. To do this, we need to know the molar mass of C4H10O:
C4H10O: (4 carbon atoms x 12.01 g/mol) + (10 hydrogen atoms x 1.01 g/mol) + (1 oxygen atom x 16.00 g/mol)
Molar mass of C4H10O = 58.12 g/mol
4. Multiply the number of moles by the molar mass of C4H10O:
0.2756 mol x 58.12 g/mol = 16.05 g
Therefore, approximately 16.05 grams of C4H10O can be melted by 2.0 x 10^3 J of energy.
To find the number of grams of C4H10O that can be melted by a given amount of energy, we need to calculate the molar energy required to melt the substance, and then use that value to determine the mass.
First, convert the given heat of fusion (ΔHfus) from kJ/mol to J/mol:
ΔHfus = 7.27 kJ/mol = 7.27 × 10^3 J/mol
Next, determine the molar mass of C4H10O (butanol):
C: 12.01 g/mol (1 atom)
H: 1.01 g/mol (10 atoms)
O: 16.00 g/mol (1 atom)
Total molar mass = (12.01 × 4) + (1.01 × 10) + 16.00 = 74.14 g/mol
Now, use the molar energy (ΔHfus) to calculate the number of moles of C4H10O that can be melted:
ΔHfus = 7.27 × 10^3 J/mol
Energy (J) = 2.0 × 10^3 J
Moles of C4H10O = Energy (J) / ΔHfus (J/mol)
Moles of C4H10O = (2.0 × 10^3 J) / (7.27 × 10^3 J/mol)
Finally, use the moles of C4H10O to find the grams:
Grams of C4H10O = Moles of C4H10O × Molar mass of C4H10O
Grams of C4H10O = (2.0 × 10^3 J) / (7.27 × 10^3 J/mol) × 74.14 g/mol
Calculate the final answer to find the number of grams of C4H10O that can be melted by 2.0 × 10^3 J.