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1 year ago

Calculate the heat energy required to melt 4kg of ice when the specific latent heat of fusion of water is 334,000 J/kg.

Chemistry

2 answers:

loris [4]1 year ago

8 0

$\bold{\huge{\blue{\underline{ Solution}}}}$

We have given in the question that, 

4kg of ice melts at the specific latent heat of fusion of water is 334,000 J/kg .

We know that,

Amount of heat required = Mass * specific heat * change in temperature

[ Specific Latent heat of fusion  is the amount of heat required to change one mole of substance from solid to liquid phase without changing in temperature .]

But, For complete melting of substance without change in temperature 

Amount of heat required = Mass * Specific latent heat of fusion

Subsitute the required values, 

$\sf{\red{ Q = MCl}}$

Where, 

Q = Amount of heat required
M = Mass of the substance
Cl = Specific latent heat

Now, 

$\sf{ Q = 4 × 334000}$

$\sf{ Q = 1336000 J }$

$\sf{ Q = 1336 KJ }$

Hence, The amount of heat required to melt 4kg ice is 1336KJ

$\bold{\red{ Option\: A \:is\: correct }}$

Setler79 [48]1 year ago

7 0

Taking into account the definition of calorimetry and latent heat, the heat energy required to melt 4 kg of ice when the specific latent heat of fusion of water is 334,000 $\frac{J}{kg}$ is 1,336 kJ.

<h3>Calorimetry</h3>

Calorimetry is the measurement and calculation of the amounts of heat exchanged by a body or a system.

<h3>Latent heat</h3>

Latent heat is defined as the energy required by a quantity of substance to change state.

When this change consists of changing from a solid to a liquid phase, it is called heat of fusion and when the change occurs from a liquid to a gaseous state, it is called heat of vaporization.

The heat Q that is necessary to provide for a mass m of a certain substance to change phase is equal to

Q = m×L

where L is called the latent heat of the substance and depends on the type of phase change.

<h3>Heat energy required to melt ice</h3>

In this case, you know:

m= 4 kg
L= specific latent heat of fusion of water= 334,000 $\frac{J}{kg}$

Replacing in the expression for latent heat:

Q = 4 kg× 334,000 $\frac{J}{kg}$

Solving:

Q= 1,336,000 J= 1,336 kJ (being 1,000 J= 1 kJ)

Finally, the correct answer is the first option: the heat energy required to melt 4 kg of ice when the specific latent heat of fusion of water is 334,000 $\frac{J}{kg}$ is 1,336 kJ.

Learn more about calorimetry:

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What is the vapor pressure of the solution if 35.0 g of water is dissolved in 100.0 g of ethyl alcohol at 25 ∘C? The vapor press

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Answer: The vapor pressure of the solution is 43.55 mmHg

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To calculate the number of moles, we use the equation:

$\text{Number of moles}=\frac{\text{Given mass}}{\text{Molar mass}}$ .....(1)

For water:

Given mass of water = 35.0 g

Molar mass of water = 18 g/mol

Putting values in equation 1, we get:

$\text{Moles of water}=\frac{35.0g}{18g/mol}=1.944mol$

For ethyl alcohol:

Given mass of ethyl alcohol = 100.0 g

Molar mass of ethyl alcohol = 46 g/mol

Putting values in equation 1, we get:

$\text{Moles of ethyl alcohol}=\frac{100.0g}{46g/mol}=2.174mol$

Total moles of solution = [1.944 = 2.174] moles = 4.118 moles

Mole fraction of a substance is given by:

$\chi_A=\frac{n_A}{n_A+n_B}$

For water:

$\chi_{\text{water}}=\frac{n_{\text{water}}}{n_{\text{water}}+n_{\text{ethyl alcohol}}}$

$\chi_{water}=\frac{1.944}{4.118}=0.472$

For ethyl alcohol:

$\chi_{\text{ethyl alcohol}}=\frac{n_{\text{ethyl alcohol}}}{n_{\text{water}}+n_{\text{ethyl alcohol}}}$

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To calculate the vapor pressure of the solution, we use the law given by Dalton, which is:

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