A mixture of C3H8 and C2H2 has a mass of 2.6g . It is burned in excess O2 to form a mixture of water and carbon dioxide that contains 1.6 times as many moles of CO2 as of water.
Find the mass of C2H2 in the original mixture.
Why did the C3H8 and C2H2 go to couples therapy?
Because they couldn't find a balance in their relationship!
But let's get to the math.
First, let's assume the mass of C3H8 is x grams and the mass of C2H2 is y grams.
Since the total mass of the mixture is 2.6g, we have the equation:
x + y = 2.6g
Next, let's calculate the moles of CO2 and water formed when the mixture is burned.
Since the ratio of CO2 to water is 1.6, we have the equation:
moles of CO2 = 1.6 * moles of water
Now, let's convert the mass of C3H8 and C2H2 to moles.
The molecular weight of C3H8 is 44g/mol, so the moles of C3H8 can be calculated as x / 44.
The molecular weight of C2H2 is 26g/mol, so the moles of C2H2 can be calculated as y / 26.
Using stoichiometry, the moles of CO2 formed can be calculated as (2 * moles of C3H8) + (2 * moles of C2H2).
The moles of water formed can be calculated as (4 * moles of C3H8) + (2 * moles of C2H2).
Therefore, we have the equation:
(2 * moles of C3H8) + (2 * moles of C2H2) = 1.6 * ((4 * moles of C3H8) + (2 * moles of C2H2))
Simplifying the equation, we get:
2 * (x / 44) + 2 * (y / 26) = 1.6 * (4 * (x / 44) + 2 * (y / 26))
Solving this equation will give us the values of x and y, which represent the mass of C3H8 and C2H2 respectively.
I hope this explanation didn't leave you feeling too burned out!
To find the mass of C2H2 in the original mixture, we need to follow these steps:
Step 1: Calculate the moles of CO2 and water produced.
Step 2: Determine the ratio of moles between CO2 and water.
Step 3: Calculate the moles of C2H2 and C3H8 in the original mixture.
Step 4: Convert the moles of C2H2 to mass.
Let's start with step 1:
Step 1: Calculate the moles of CO2 and water produced.
The balanced chemical equation for the reaction of C3H8 and C2H2 with O2 to form CO2 and H2O is:
C3H8 + C2H2 + 5O2 -> 3CO2 + 2H2O
From the equation, we can see that 1 mole of C3H8 reacts with 1 mole of C2H2, producing 3 moles of CO2 and 2 moles of H2O.
Let's assume x is the number of moles of water produced. Therefore, the number of moles of CO2 produced will be 1.6 times x.
So the moles of CO2 produced will be 1.6x, and the moles of H2O produced will be x.
Step 2: Determine the ratio of moles between CO2 and water.
Given that the moles of CO2 produced is 1.6 times the moles of water produced, we can write:
1.6x / x = 1.6
So the ratio of moles between CO2 and water is 1.6:1.
Step 3: Calculate the moles of C2H2 and C3H8 in the original mixture.
Since the total mass of the mixture is given as 2.6g, we need to find the mass of C2H2 and C3H8 separately.
Let's assume the mass of C2H2 is y grams and the mass of C3H8 is (2.6 - y) grams.
To calculate the moles of C2H2 and C3H8, we need to use their respective molar masses.
The molar mass of C2H2 is calculated as follows:
12.01 g/mol (C) + 2 * 1.01 g/mol (H) = 26.04 g/mol
The molar mass of C3H8 is calculated as follows:
3 * 12.01 g/mol (C) + 8 * 1.01 g/mol (H) = 44.11 g/mol
Now we can calculate the moles of C2H2 and C3H8:
Moles of C2H2 = y (mass) / 26.04 (molar mass)
Moles of C3H8 = (2.6 - y) (mass) / 44.11 (molar mass)
Step 4: Convert the moles of C2H2 to mass.
Since we have the moles of C2H2, we can now convert it to mass using the molar mass.
Mass of C2H2 = Moles of C2H2 * Molar mass of C2H2
Now, we can combine all these steps to find the mass of C2H2 in the original mixture.
To find the mass of C2H2 in the original mixture, we need to use the given information and apply stoichiometry.
First, let's set up a balanced chemical equation for the combustion reaction of the mixture:
C3H8 + C2H2 + O2 -> CO2 + H2O
From the equation, we can see that for every 1 mole of C2H2, we will have 1 mole of CO2.
Let's assume the number of moles of water in the mixture is x.
So, the number of moles of CO2 will be 1.6x (since it is 1.6 times as many moles as water).
Now, we can calculate the number of moles of C3H8 by subtracting the moles of C2H2 and CO2 from the total moles of the mixture:
moles of C3H8 = total moles - moles of C2H2 - moles of CO2
Since the total mass of the mixture is given as 2.6g, we can assume that it represents the total moles:
total moles = mass / molar mass
The molar mass of C3H8 (propane) is 44.1 g/mol, while the molar mass of C2H2 (acetylene) is 26.04 g/mol.
Now, let's calculate the number of moles of C3H8:
moles of C3H8 = 2.6g / 44.1 g/mol
Next, we substitute the given information into the equation:
2.6g / 44.1 g/mol = (2.6 - moles of C2H2 - 1.6x - x) / 26.04 g/mol
From here, we can solve for x, which represents the number of moles of water in the mixture.
Solving the equation will give us x = 0.0577 moles.
Since the number of moles of CO2 is 1.6 times the number of moles of water, we have:
moles of CO2 = 1.6 * x = 1.6 * 0.0577 = 0.09232 moles CO2
Finally, to find the mass of C2H2, we use the equation:
mass of C2H2 = moles of C2H2 * molar mass of C2H2
mass of C2H2 = moles of C2H2 * 26.04 g/mol
Plugging in the values, we get:
mass of C2H2 = (2.6 - moles of C3H8 - moles of CO2 - moles of water) * 26.04 g/mol
mass of C2H2 = (2.6 - 0.0577 - 0.09232 - 0.0577) * 26.04 g/mol
mass of C2H2 = 2.39234 g
Therefore, the mass of C2H2 in the original mixture is approximately 2.39 grams.