ethanol melts at -114c the enthalpy of fusion 5.02 kj/mol the specific heats of solid and liquid ethanol are 0.97 and 2.3 respectively . how much heat is needed to convert 25 g of solid etanol ay -135c to liquid ethanol at -50c?

6.91

To calculate the amount of heat needed to convert a substance from a solid to a liquid state, you need to consider two steps: first, heating the solid ethanol from its initial temperature to its melting point, and second, melting the solid ethanol to liquid ethanol at its melting point. Then, you also need to consider heating the liquid ethanol to the final temperature.

Step 1: Heating the solid ethanol to its melting point
q1 = m × C × ΔT
where:
q1 is the heat absorbed (in joules),
m is the mass of the solid ethanol (in grams),
C is the specific heat capacity of solid ethanol (in J/g·°C), and
ΔT is the change in temperature (final temperature - initial temperature).

q1 = 25 g × 0.97 J/g·°C × (−114 °C − (−135 °C))

Step 2: Melting the solid ethanol to liquid ethanol
q2 = ΔHf × moles
where:
q2 is the heat absorbed (in joules),
ΔHf is the enthalpy of fusion (in J/mol), and
moles is the number of moles of ethanol.

To find the number of moles of ethanol, we need to use its molar mass, which is 46.07 g/mol.

moles = mass / molar mass = 25 g / 46.07 g/mol

q2 = 5.02 kJ/mol × (25 g / 46.07 g/mol) × 1000 J/kJ

Step 3: Heating the liquid ethanol to the final temperature
q3 = m × C × ΔT
where:
q3 is the heat absorbed (in joules),
m is the mass of the liquid ethanol (in grams),
C is the specific heat capacity of liquid ethanol (in J/g·°C), and
ΔT is the change in temperature (final temperature - melting point).

q3 = 25 g × 2.3 J/g·°C × (−50 °C − (−114 °C))

The total heat required is the sum of the heat absorbed in each step.

Total heat = q1 + q2 + q3

Calculate each step using the given values and perform the arithmetic.

To calculate the heat needed to convert 25 g of solid ethanol (-135°C) to liquid ethanol (-50°C), we need to consider three different steps:

Step 1: Heat required to raise the temperature of solid ethanol from -135°C to its melting point, -114°C.
Step 2: Heat required to convert the solid ethanol into liquid ethanol at its melting point (-114°C).
Step 3: Heat required to raise the temperature of the liquid ethanol from -114°C to -50°C.

Let's calculate each step one by one:

Step 1: Heating the solid ethanol from -135°C to -114°C
The specific heat capacity of solid ethanol is 0.97 J/g°C.
Therefore, the heat required to raise the temperature can be calculated using the formula:

Q1 = m * c * ΔT1

where:
Q1 = heat required
m = mass of the substance (25 g)
c = specific heat capacity (0.97 J/g°C)
ΔT1 = change in temperature (Tfinal - Tinitial)

ΔT1 = -114°C - (-135°C) = 21°C

Plugging the values into the formula:

Q1 = 25 g * 0.97 J/g°C * 21°C
Q1 = 496.5 J

Step 2: Melting the solid ethanol at -114°C
The enthalpy of fusion (heat required to convert 1 mole of solid into liquid) is given as 5.02 kJ/mol.

To calculate the heat required to melt 25 g of solid ethanol, we need to convert the mass into moles:

n = mass / molar mass
n = 25 g / 46.07 g/mol (molar mass of ethanol)
n = 0.543 mol

The heat required to melt the solid ethanol can be calculated using the formula:

Q2 = n * ΔHf

where:
Q2 = heat required
n = moles of substance (0.543 mol)
ΔHf = enthalpy of fusion (5.02 kJ/mol)

Plugging the values into the formula:

Q2 = 0.543 mol * 5.02 kJ/mol
Q2 = 2.724 kJ = 2724 J

Step 3: Heating the liquid ethanol from -114°C to -50°C
The specific heat capacity of liquid ethanol is 2.3 J/g°C.
Therefore, the heat required to raise the temperature can be calculated using the formula:

Q3 = m * c * ΔT2

where:
Q3 = heat required
m = mass of the substance (25 g)
c = specific heat capacity (2.3 J/g°C)
ΔT2 = change in temperature (Tfinal - Tinitial)

ΔT2 = -50°C - (-114°C) = 64°C

Plugging the values into the formula:

Q3 = 25 g * 2.3 J/g°C * 64°C
Q3 = 3680 J

Now, let's calculate the total heat required by adding the results from each step:

Total Heat = Q1 + Q2 + Q3
Total Heat = 496.5 J + 2724 J + 3680 J
Total Heat = 6900.5 J

Therefore, approximately 6900.5 J of heat is needed to convert 25 g of solid ethanol at -135°C to liquid ethanol at -50°C.