Respuesta :
Answer: 66.7 kJ
Explanation:
1) The amounf of heat to melt an amount of water (H₂O s) is equal to the amount of water times the melting latent heat.
2) The melting latent heat of water is found in tables or a textbook. It is 6.01 kJ / mol
3) Since, the melting latent heat of water found is per mol, we have to convert the givent mass of water into number of moles:
number of moles = mass in grams / molar mass = 200 g / 18.01 g/mol = 11.1 mol
4) Calculation of the heat required:
Heat = 11.1 moles × 6.01 kJ / mol = 66.7 kJ.
Explanation:
1) The amounf of heat to melt an amount of water (H₂O s) is equal to the amount of water times the melting latent heat.
2) The melting latent heat of water is found in tables or a textbook. It is 6.01 kJ / mol
3) Since, the melting latent heat of water found is per mol, we have to convert the givent mass of water into number of moles:
number of moles = mass in grams / molar mass = 200 g / 18.01 g/mol = 11.1 mol
4) Calculation of the heat required:
Heat = 11.1 moles × 6.01 kJ / mol = 66.7 kJ.
[tex]\boxed{{\text{121}}{\text{.188 kJ}}}[/tex] of energy is required to melt the sample completely.
Further explanation:
Amount of energy that is required to melt a solid substance at its melting point is known as heat of fusion. Here, the state of substance changes from solid to liquid. It is denoted by [tex]\Delta {H_{\text{f}}}[/tex].
The formula to calculate the amount of energy is as follows:
[tex]{\text{Q}} = {\text{n}}\Delta {H_{\text{f}}}[/tex] ...... (1)
Here,
Q is the amount of energy.
n is the number of moles of water.
[tex]\Delta {H_{\text{f}}}[/tex] is the heat of fusion of ice.
The moles of water are calculated by the following formula:
[tex]{\text{Moles of water}} = \dfrac{{{\text{Given mass of water}}}}{{{\text{Molar mass of water}}}}[/tex] ...... (2)
The formula to calculate the molar mass of water [tex]\left( {{{\text{H}}_{\text{2}}}{\text{O}}} \right)[/tex] is as follows:
[tex]{\text{Molar mass of water}} = \left[ {2\left( {{\text{Atomic mass of H}}} \right) + 1\left( {{\text{Atomic mass of O}}} \right)} \right][/tex] ...... (3)
The atomic mass of H is 1.01 g
The atomic mass of O is 15.99 g.
Substitute these values in equation (3).
[tex]\begin{aligned}{\text{Molar mass of water}} &= \left[ {2\left( {{\text{1}}{\text{.01 g}}} \right) + 1\left( {{\text{15}}{\text{.99 g}}} \right)} \right]\\&= 18.01{\text{ g/mol}}\\\end{aligned}[/tex]
The given mass of water is 200 g.
The molar mass of water is 18.01 g/mol.
Substitute these values in equation (2).
[tex]\begin{aligned}{\text{Moles of water}} &= \frac{{200{\text{ g}}}}{{{\text{18}}{\text{.01 g/mol}}}}\\&= 11.105{\text{ mol}} \\&\approx {\text{11}}{\text{.11 mol}}\\\end{aligned}[/tex]
The number of moles of water is 11.11 g/mol.
The value of [tex]\Delta {H_{\text{f}}}[/tex] is 6.01 kJ/mol.
Substitute these values in equation (1).
[tex]\begin{aligned}{{\text{Q}}_1} U&= \left( {{\text{11}}{\text{.11 mol}}} \right)\left( {\frac{{6.01{\text{ kJ}}}}{{1{\text{ mol}}}}} \right)\\&= 66.77{\text{ kJ}}\\\end{aligned}[/tex]
Learn more:
- What is the enthalpy of the given reaction? https://brainly.com/question/10412973
- Find the enthalpy of decomposition of 1 mole of MgO: https://brainly.com/question/2416245
Answer details:
Grade: Senior School
Chapter: Thermodynamics
Subject: Chemistry
Keywords: Q, energy, n, 200 g, 18.01 g/mol, atomic mass of H, atomic mass of O, 15.99 g, 1.01 g, 66.77 kJ.
