In a car engine, gasoline (represented by C8H18) does not burn completely, and some CO forms along with CO2 and H2O. If 5 percent of the gasoline forms CO,
A)What is the ratio of CO2 to CO molecules in the exhaust?
B)What is the mass ratio of CO2 to CO?
C)What percentage of gasoline must form CO for the mass ratio of CO2 to CO to be 1/1?
A) Well, if 5 percent of the gasoline forms CO, we can assume that the other 95 percent forms CO2. So for every molecule of CO, there are 19 molecules of CO2. Therefore, the ratio of CO2 to CO molecules in the exhaust is 19:1.
B) Now, let's talk mass. In terms of atomic mass, carbon dioxide (CO2) has a molar mass of 44 grams/mol, and carbon monoxide (CO) has a molar mass of 28 grams/mol. So the mass ratio of CO2 to CO would be 44:28, which can be simplified to 11:7.
C) To find out the percentage of gasoline that must form CO for the mass ratio of CO2 to CO to be 1/1, we need to set up an equation. Let's call the percentage of gasoline that forms CO "x". This means that the percentage of gasoline that forms CO2 would be (100 - x).
Now, using the molar masses, we can say that (100 - x) * 44 grams of CO2 = x * 28 grams of CO.
Simplifying that equation, we get 4400 - 44x = 28x.
Bringing like terms to one side, we have 72x = 4400.
Dividing both sides by 72, we find that x ≈ 61.1.
So, approximately 61.1 percent of the gasoline must form CO for the mass ratio of CO2 to CO to be 1/1.
Remember, these are all approximate answers, so take them with a grain of clownish humor!
To solve these questions, we need to consider the balanced chemical equation for the combustion of gasoline (C8H18):
C8H18 + O2 -> CO2 + CO + H2O
Let's assume we have 100 moles of gasoline (C8H18).
A) To find the ratio of CO2 to CO molecules in the exhaust, we need to determine the number of moles of each compound produced.
Here's a breakdown of the balanced equation:
1 mole of C8H18 produces 8 moles of CO2
1 mole of C8H18 produces 1 mole of CO
Since 5% of the gasoline forms CO, only 5 moles of CO are produced. Therefore, the ratio of CO2 to CO molecules in the exhaust is 8:5.
B) To find the mass ratio of CO2 to CO, we need to consider the molar masses of CO2 and CO.
The molar mass of CO2 is 44 g/mol (12 g/mol for carbon + 2 * 16 g/mol for oxygen).
The molar mass of CO is 28 g/mol (12 g/mol for carbon + 16 g/mol for oxygen).
Using the ratio from part A (8:5), we can calculate the mass ratio:
Mass Ratio = (8 * molar mass of CO2) / (5 * molar mass of CO)
Mass Ratio = (8 * 44 g/mol) / (5 * 28 g/mol)
Mass Ratio = 352 g / 140 g
Mass Ratio = 2.51
Therefore, the mass ratio of CO2 to CO is approximately 2.51:1.
C) To find the percentage of gasoline that must form CO for the mass ratio of CO2 to CO to be 1/1, we can set up an equation.
Let's assume x represents the percentage of gasoline that forms CO.
The percentage of gasoline that forms CO2 can be calculated as (100 - x) since the remaining gasoline must form CO2.
Using the molar ratios from the balanced equation:
(100 - x)% of the gasoline produces (8/9) * (100 - x) moles of CO2
x% of the gasoline produces (1/9) * x moles of CO
Since we want the mass ratio of CO2 to CO to be 1/1, we can set up the equation:
((8/9) * (100 - x) * molar mass of CO2) / ((1/9) * x * molar mass of CO) = 1
Simplifying the equation:
(8/9) * (100 - x) * molar mass of CO2 = (1/9) * x * molar mass of CO
Now let's solve for x:
8 * (100 - x) * 44 = x * 28
352 * (100 - x) = 7x
35200 - 352x = 7x
35200 = 359x
x ≈ 98.05
Therefore, approximately 98.05% of the gasoline must form CO for the mass ratio of CO2 to CO to be 1/1.
To answer these questions, we need to understand the chemical equation for the incomplete combustion of gasoline and then use stoichiometry to determine the ratios and percentages.
The balanced chemical equation for the incomplete combustion of gasoline (C8H18) can be written as:
C8H18 + xO2 -> yCO2 + zCO + wH2O
A) To find the ratio of CO2 to CO molecules in the exhaust, we need to determine the values of y and z in the balanced chemical equation.
Since 5% of the gasoline forms CO, it means that 95% will form other products, including CO2. From this information, we can conclude that the ratio of CO2 to CO molecules is 95:5 or 19:1.
B) To calculate the mass ratio of CO2 to CO, we need to know the molar masses of CO2 and CO.
The molar mass of CO2 is 44 g/mol, and the molar mass of CO is 28 g/mol. Using these molar masses, we can determine the mass ratio of CO2 to CO.
Since the ratio of CO2 to CO is 19:1 (from part A), we can assign a value of 19x to CO2 and x to CO. The mass ratio can be calculated as follows:
Mass ratio of CO2 to CO = (19x * molar mass of CO2) / (x * molar mass of CO)
C) To determine the percentage of gasoline that must form CO for the mass ratio of CO2 to CO to be 1/1, we can set up an equation using the mass ratio from part B and solve for x.
1 = (19x * molar mass of CO2) / (x * molar mass of CO)
By rearranging the equation and solving for x, we can find the percentage of gasoline that must form CO.
It is important to note that the actual values of y, z, w, and x will be determined through experimental data and may vary slightly from the theoretical values calculated here. The calculations provided serve as a theoretical understanding based on the given information.