CH₄ Combustion: Calculate Mass For Water Heating
Hey guys! Let's dive into a super interesting chemistry problem today. We're going to figure out how much methane (CH₄) we need to burn to heat up some water. This involves understanding enthalpy of combustion, specific heat capacity, and good ol' stoichiometry. Buckle up, it's gonna be a fun ride!
Understanding the Problem
First, let’s break down what we know. The problem gives us the standard enthalpy of combustion (ΔH°C) for methane (CH₄), which is 800 kJ/mol. This means when one mole of methane is completely burned, it releases 800 kilojoules of heat. That's a lot of energy! We also know we want to heat 1000 grams of water from 30°C to 90°C. To do this, we need to figure out how much heat is required, and then how much methane we need to burn to produce that heat.
We're also provided with some handy constants: the atomic masses of carbon (Ar C = 12) and hydrogen (H = 1), which we'll use to calculate the molar mass of methane, and the specific heat capacity of water (4.2 J/g°C). This tells us how much energy is needed to raise the temperature of one gram of water by one degree Celsius. This is crucial for our calculations.
The core of this problem lies in connecting the heat released by combustion (a chemical process) to the heat absorbed by water (a physical process). We'll use the enthalpy of combustion to find out how much heat is released per mole of methane burned, and the specific heat capacity to calculate how much heat is needed to raise the water's temperature. By equating these two, we can find the amount of methane needed. Remember, chemistry is all about making connections!
Calculating the Heat Required to Raise Water Temperature
The first step in solving this problem is figuring out just how much heat we need to pump into that water to raise its temperature from 30°C to 90°C. We're going to use a nifty little formula for this, which you might remember from your chemistry or physics classes:
Q = mcΔT
Where:
- Q is the heat energy (in Joules)
- m is the mass of the water (in grams)
- c is the specific heat capacity of water (4.2 J/g°C)
- ΔT is the change in temperature (in °C)
Let's plug in the values we know:
- m = 1000 grams
- c = 4.2 J/g°C
- ΔT = 90°C - 30°C = 60°C
So, Q = 1000 g * 4.2 J/g°C * 60°C
Q = 252,000 Joules
Whoa, that's a lot of Joules! But remember, the enthalpy of combustion is given in kilojoules (kJ), so let’s convert Joules to kJ by dividing by 1000:
Q = 252,000 J / 1000 = 252 kJ
Okay, so we now know that we need 252 kJ of heat to warm up our water. Now we're cooking with gas! (Well, actually, we're trying to cook with methane, but you get the idea.)
Determining Moles of CH₄ Required
Alright, now that we know how much heat we need (252 kJ), we can figure out how many moles of methane (CH₄) we need to burn to get that much heat. Remember, the problem tells us the standard enthalpy of combustion (ΔH°C) of CH₄ is 800 kJ/mol. This means that burning one mole of CH₄ releases 800 kJ of heat. This is our key conversion factor!
To find the number of moles of CH₄ needed, we'll set up a simple proportion:
(Moles of CH₄) / (Heat Required) = (1 mol CH₄) / (800 kJ)
Let's plug in the heat required (252 kJ):
(Moles of CH₄) / (252 kJ) = (1 mol CH₄) / (800 kJ)
Now, we just solve for moles of CH₄:
Moles of CH₄ = (252 kJ * 1 mol CH₄) / 800 kJ
Moles of CH₄ = 0.315 moles
Fantastic! We've calculated that we need to burn 0.315 moles of CH₄ to generate the 252 kJ of heat required to raise the water temperature. We're getting closer to our final answer!
Calculating the Mass of CH₄
The problem asks for the mass of CH₄, not the number of moles. No sweat! We've got the number of moles, and we know how to convert moles to grams using the molar mass.
First, we need to calculate the molar mass of CH₄. Remember, the molar mass is the sum of the atomic masses of all the atoms in the molecule. We're given the atomic masses of carbon (Ar C = 12) and hydrogen (H = 1).
CH₄ has one carbon atom and four hydrogen atoms, so its molar mass is:
Molar mass of CH₄ = (1 * 12) + (4 * 1) = 12 + 4 = 16 g/mol
Now, we can use the following formula to convert moles to grams:
Mass = Moles * Molar Mass
We know the number of moles of CH₄ (0.315 moles) and the molar mass (16 g/mol), so let's plug them in:
Mass of CH₄ = 0.315 moles * 16 g/mol
Mass of CH₄ = 5.04 grams
Final Answer
Drumroll, please! We've reached the end of our calculation journey.
To raise the temperature of 1000 grams of water from 30°C to 90°C, you need to burn approximately 5.04 grams of CH₄.
Woohoo! We did it! We successfully tackled this thermo-chemical problem by breaking it down into smaller, manageable steps. Remember, chemistry problems might seem daunting at first, but with a little bit of understanding and the right approach, you can conquer them all. Keep practicing, and you'll become a chemistry whiz in no time! And that’s how you’d solve this problem, folks! Keep your thinking caps on and keep exploring the world of chemistry!
