Acetone Vaporization: Heat Calculation Guide
Hey there, chemistry enthusiasts! Today, we're diving into a classic thermodynamics problem: figuring out how much heat is needed to completely vaporize a liquid sample of acetone and crank up its temperature. This isn't just some abstract concept; understanding these calculations is super important in all sorts of real-world applications, from industrial processes to lab experiments. So, buckle up, because we're about to break down the steps, the formulas, and the fun that comes with solving these types of problems.
Understanding the Problem and Key Concepts
Alright, guys, let's start with the basics. We've got a 32.16-gram sample of liquid acetone (C₃H₆O), and our mission is to turn it into vapor and then heat that vapor up to a final temperature of 67.3°C. This process actually involves a few different stages, each requiring a specific amount of energy. First, we need to heat the liquid acetone up to its boiling point. Then, we need to supply the heat necessary to change the liquid into a gas (vaporization). Finally, we need to heat the acetone vapor from its boiling point to our target temperature of 67.3°C. We'll need to use some handy-dandy formulas and data to solve this, so let's get the important things we need in this calculation. This is a multi-step process, and the total heat required will be the sum of the heat needed for each step.
Key Concepts to Keep in Mind
- Specific Heat Capacity (c): This is the amount of heat required to raise the temperature of 1 gram of a substance by 1 degree Celsius. Different substances have different specific heat capacities. For liquid acetone, we'll need to use its specific heat capacity. The amount of heat needed to raise the temperature of a substance is calculated using the formula: q = mcΔT. Where q is the heat, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature.
- Enthalpy of Vaporization (ΔHvap): This is the amount of heat required to vaporize 1 mole of a substance at its boiling point. It is also known as the heat of vaporization. This is the amount of energy required to overcome the intermolecular forces holding the liquid molecules together and change them into a gas. This value is usually given in kJ/mol. We will need to convert the amount of acetone from grams to moles.
- Boiling Point: The temperature at which a liquid changes into a gas at a given pressure. We need the boiling point of acetone to know the temperature at which vaporization occurs. Acetone boils at 56.05°C at standard atmospheric pressure. This is the temperature at which we will add the heat of vaporization.
Step-by-Step Calculation
Okay, time to get down to business and crunch some numbers! We'll break this problem into three main parts, calculating the heat for each stage and then adding them together to find the total heat required.
Step 1: Heating Liquid Acetone to Its Boiling Point
First, we need to calculate the heat required to raise the temperature of the liquid acetone from its initial temperature (which we assume to be room temperature, around 25°C) to its boiling point (56.05°C). We'll use the following formula:
q = mcΔT
Where:
- q = heat (in Joules) - This is what we are trying to find.
- m = mass of acetone (32.16 g)
- c = specific heat capacity of liquid acetone (2.18 J/g·°C)
- ΔT = change in temperature (boiling point - initial temperature = 56.05°C - 25°C = 31.05°C)
Plugging in the values:
q = (32.16 g) * (2.18 J/g·°C) * (31.05°C) q ≈ 2177.73 J
So, it takes approximately 2177.73 Joules to heat the liquid acetone to its boiling point.
Step 2: Vaporizing the Liquid Acetone
Next, we need to calculate the heat required to vaporize the acetone at its boiling point. This involves using the enthalpy of vaporization (ΔHvap).
- First, we need to convert the mass of acetone to moles using its molar mass (58.08 g/mol):* Moles of acetone = 32.16 g / 58.08 g/mol ≈ 0.554 mol
- We are given the enthalpy of vaporization of acetone (30.2 kJ/mol) q = moles * ΔHvap q = 0.554 mol * 30.2 kJ/mol q ≈ 16.75 kJ q ≈ 16750 J
So, it takes approximately 16750 Joules to vaporize the liquid acetone.
Step 3: Heating Acetone Vapor to 67.3°C
Now, we need to calculate the heat required to raise the temperature of the acetone vapor from its boiling point (56.05°C) to the final temperature (67.3°C). We'll use the same formula as in Step 1, but this time we'll use the specific heat capacity of acetone vapor (1.28 J/g·°C).
q = mcΔT
Where:
- q = heat (in Joules) - This is what we are trying to find.
- m = mass of acetone (32.16 g)
- c = specific heat capacity of acetone vapor (1.28 J/g·°C)
- ΔT = change in temperature (final temperature - boiling point = 67.3°C - 56.05°C = 11.25°C)
Plugging in the values:
q = (32.16 g) * (1.28 J/g·°C) * (11.25°C) q ≈ 462.72 J
So, it takes approximately 462.72 Joules to heat the acetone vapor to 67.3°C.
Step 4: Calculating the total heat
To get the total amount of heat, we add up the heat from each step:
- Heat to reach the boiling point: 2177.73 J
- Heat for vaporization: 16750 J
- Heat to reach 67.3°C: 462.72 J
Total Heat = 2177.73 J + 16750 J + 462.72 J = 19390.45 J
Conclusion
There you have it, folks! We have successfully calculated the total amount of heat required to vaporize 32.16 g of acetone and raise the temperature of the vapor to 67.3°C. The total heat required is approximately 19390.45 Joules, or 19.39 kJ. This kind of calculation is very useful in many different fields. The steps we took include calculating the heat needed to raise the temperature, the heat needed to vaporize the liquid, and the heat needed to raise the temperature again. Remember that the specific heat capacity is the amount of energy needed to increase the temperature of a substance. Also, keep in mind the importance of the enthalpy of vaporization in this calculation.
Remember to always double-check your units and make sure you're using the correct values for each substance. Keep practicing, and these calculations will become second nature! If you have questions or want to dive deeper into other chemistry topics, let me know!
