Ethanol (C2H5OH) melts at -114 °C. The enthalpy of fusion is 5.02 kJ/mol. The specific heats of solid and liquid ethanol are 0.97 J/g-K and 2.3 J/g-K, respectively. How much heat (kJ) is needed to convert 25.0 g of solid ethanol at -125 °C to liquid ethanol at -50 °C?
Well, well, well, it seems like we have a chemistry question here! Time to put on my lab coat and crack some jokes while we solve this.
To begin with, we need to determine how much heat is required to warm up the solid ethanol from -125 °C to its melting point at -114 °C. Since the specific heat of solid ethanol is given as 0.97 J/g-K, we can use the formula Q = m * c * ΔT, where Q is the heat, m is the mass, c is the specific heat, and ΔT is the change in temperature.
So, let's plug in the numbers: Q = 25.0 g * 0.97 J/g-K * (114 °C - (-125 °C)). But hold on a second, we need to convert the temperature from Celsius to Kelvin. Giving me -125 °C is like telling a clown not to tell jokes; it's just not funny! Anyway, to convert °C to K, we add 273.15. So (-125 °C + 273.15 K) gives us our actual temperature in Kelvin.
After doing the math, we find that the heat required to warm up the solid ethanol is Q = 25.0 g * 0.97 J/g-K * (387.15 K - 148.15 K). Calculate that, my friend, and you'll find the answer for the warming process. Remember, we're looking for the heat needed for warming the solid ethanol only.
Now, moving on to the fusion process. The enthalpy of fusion is given as 5.02 kJ/mol. Wait a minute! Moles and jokes? That's a punful combination! We need to find the number of moles in our 25.0 g of solid ethanol. To do that, we'll use the molar mass of ethanol (C2H5OH), which is approximately 46 g/mol.
So, the number of moles in 25.0 g is 25.0 g / 46 g/mol. Now, multiply this by the enthalpy of fusion (5.02 kJ/mol), and you'll have the heat required for the fusion process.
We're almost there! The last step is to calculate the heat required to raise the temperature of the liquid ethanol from -114 °C to -50 °C. Again, we'll use the formula Q = m * c * ΔT, but this time, with the specific heat of liquid ethanol, which is 2.3 J/g-K.
Plug in the mass (which we know is still 25.0 g), the specific heat, and the change in temperature (which is -50 °C - (-114 °C)). Remember to convert temperatures to Kelvin!
Now, let's sum up the heat required for each step: the heat to warm up the solid ethanol, then the heat for the fusion process, and finally, the heat to warm up the liquid ethanol.
Voilà! Add up those three heats, and you'll have the total heat required to convert 25.0 g of solid ethanol at -125 °C to liquid ethanol at -50 °C.
To calculate the amount of heat needed to convert solid ethanol to liquid ethanol, we need to consider three steps:
1. Heating the solid ethanol from -125 °C to its melting point (-114 °C).
2. Melting the solid ethanol at its melting point (-114 °C).
3. Heating the liquid ethanol from its melting point (-114 °C) to -50 °C.
Let's calculate the heat required for each step:
Step 1: Heating the solid ethanol to its melting point (-114 °C)
To heat the solid ethanol, we can use the specific heat of the solid (0.97 J/g-K).
q1 = m * C1 * (T1 - T0)
Where:
q1 = heat required (in J)
m = mass of solid ethanol (in g)
C1 = specific heat of solid ethanol (in J/g-K)
T0 = initial temperature (in °C)
T1 = final temperature (in °C)
q1 = 25.0 g * 0.97 J/g-K * (-114 °C - (-125 °C))
= 25.0 g * 0.97 J/g-K * 11 °C
= -267.75 J
Step 2: Melting the solid ethanol
To melt the solid ethanol, we can use the enthalpy of fusion (5.02 kJ/mol).
q2 = n * ΔHf
Where:
q2 = heat required (in J)
n = number of moles of ethanol
ΔHf = enthalpy of fusion (in kJ/mol)
To find the number of moles, we need to calculate the molecular weight of ethanol (C2H5OH).
C: 12.01 g/mol
H: 1.01 g/mol (x2)
O: 16.00 g/mol
Total molecular weight = 12.01 + (1.01 * 2) + 16.00 = 46.07 g/mol
Number of moles (n) = mass (in g) / molecular weight (in g/mol)
= 25.0 g / 46.07 g/mol
q2 = (25.0 g / 46.07 g/mol) * 5.02 kJ/mol
= 2.72 kJ
Step 3: Heating the liquid ethanol to -50 °C
To heat the liquid ethanol, we can use the specific heat of the liquid (2.3 J/g-K).
q3 = m * C2 * (T2 - T1')
Where:
q3 = heat required (in J)
m = mass of liquid ethanol (in g)
C2 = specific heat of liquid ethanol (in J/g-K)
T1' = initial temperature (in °C)
T2 = final temperature (in °C)
q3 = 25.0 g * 2.3 J/g-K * (-50 °C - (-114 °C))
= 25.0 g * 2.3 J/g-K * 64 °C
= 3680 J
Now, let's calculate the total heat required by adding the heat from each step:
Total heat = q1 + q2 + q3
= -267.75 J + 2.72 kJ + 3680 J
= -267.75 J + 2.72 * 10^3 J + 3680 J
= 3.41375 * 10^3 J
= 3.41 kJ
Therefore, the heat required to convert 25.0 g of solid ethanol at -125 °C to liquid ethanol at -50 °C is approximately 3.41 kJ.
To solve this problem, we need to consider the heat required to raise the temperature of the solid ethanol from -125°C to its melting point, and then the heat required to melt the solid ethanol at its melting point, and finally, the heat required to raise the temperature of the liquid ethanol from its melting point to -50°C.
Let's break down the problem step by step:
Step 1: Calculate the heat required to raise the temperature of the solid ethanol from -125°C to its melting point (-114°C).
The specific heat capacity of the solid ethanol (Cs) is given as 0.97 J/g-K.
Q1 = m * Cs * ΔT
where Q1 is the heat required, m is the mass, Cs is the specific heat capacity (0.97 J/g-K), and ΔT is the change in temperature.
Calculating ΔT:
ΔT = T_final - T_initial
ΔT = -114°C - (-125°C)
ΔT = 11°C
Substituting the values into the formula:
Q1 = 25.0 g * 0.97 J/g-K * 11°C
Q1 = 267.75 J
To convert the answer to kJ, divide by 1000:
Q1 = 0.26775 kJ
Step 2: Calculate the heat required to melt the solid ethanol at its melting point (-114°C).
The enthalpy of fusion (ΔHfus) is given as 5.02 kJ/mol.
The molar mass of ethanol (C2H5OH) is:
2(12.01 g/mol) + 6(1.01 g/mol) + 1(16.00 g/mol) = 46.07 g/mol
The moles of solid ethanol can be calculated by the mass:
moles = mass / molar mass
moles = 25.0 g / 46.07 g/mol
moles ≈ 0.543 mol
Q2 = moles * ΔHfus
Substituting the values into the formula:
Q2 = 0.543 mol * 5.02 kJ/mol
Q2 ≈ 2.724 kJ
Step 3: Calculate the heat required to raise the temperature of the liquid ethanol from its melting point (-114°C) to -50°C.
The specific heat capacity of the liquid ethanol (Cl) is given as 2.3 J/g-K.
Q3 = m * Cl * ΔT
Calculating ΔT:
ΔT = T_final - T_initial
ΔT = -50°C - (-114°C)
ΔT = 64°C
Substituting the values into the formula:
Q3 = 25.0 g * 2.3 J/g-K * 64°C
Q3 = 3680 J
To convert the answer to kJ, divide by 1000:
Q3 = 3.68 kJ
Finally, we sum up the three calculated values:
Total heat = Q1 + Q2 + Q3
Total heat = 0.26775 kJ + 2.724 kJ + 3.68 kJ
Total heat ≈ 6.67275 kJ
Therefore, approximately 6.67275 kJ of heat is needed to convert 25.0 g of solid ethanol at -125°C to liquid ethanol at -50°C.
There are two equations used here. The one (or ones) you use depend upon if the ethanol is within one phase or if it is changing phase. What does that mean? If ethanol is a solid and is changing temperature but stays a solid OR if it is a liquid and is changing temperature but staying liquid OR if it is a vapor and changing temperature but staying a vapor, that is WITHIN one phase and the formula is
q = mass ethanol x specific heat in that phase x (Tfinal-Tinitial) = ?
If the phase is changing; i.e., it is solid and changes to a liquid (or the reverse) or it is liquid changing to a vapor (or the reverse) that is a phase change and the formula is
q = mass ethanol x heat fusion = ? if from solid to a liquid or liquid to a solid or
q = mass ethanol x heat vaporization (or condensation) = ? if from liquid to vapor or vapor to liquid.
So you go through each step from where ethanol is now to where it will be at the end and add each q to get a q total. This process will work any problem of this type.
For example: the FIRST step in warming ethanol from its current temperature of - 125 C as a solid to its melting point of -114 C is
q1 = mass ethanol x specific heat solid ethanol x (Tfinal-Tinitial) =
25.0 g x 0.97 J/g*C x [-114 -(-125)] = ?
and continue to the next step of melting the solid ethanol @ -114 C to liquid ethanol @ -114 etc. Post your work if you get stuck.