Question

4 moles of carbon plus 3 moles of oxygen weigh 96 grams. 2 moles of carbon plus 5 moles of

oxygen weigh 104 grams. From these values, determine the molar mass of carbon and
oxygen. Show your working.

Answer 1

Using the given mass and mole equations, we can set up a system of equations to solve for the unknown molar masses. After substituting and simplifying, we find that the molar mass of carbon is 12 grams/mole and the molar mass of oxygen is 16 grams/mole.

Step-by-step explanation:

To determine the molar mass of carbon and oxygen, we can set up two equations based on the given information:

Equation for 4 moles of carbon and 3 moles of oxygen (96 grams total):

• 4C + 3O = 96 grams

Equation for 2 moles of carbon and 5 moles of oxygen (104 grams total):

• 2C + 5O = 104 grams

Let's denote C as the molar mass of carbon and O as the molar mass of oxygen. We then have the following system of linear equations:

• 4C + 3O = 96
• 2C + 5O = 104

Solving this system of equations:

1. Multiply the first equation by 2, 2(4C) + 2(3O) = 2(96) ==> 8C + 6O = 192
2. Taking that result and subtracting the second equation from it, we get 8C + 6O - (2C + 5O) = 192 - 104
3. This simplifies to 6C + O = 88
4. Now, from the first equation, solve for O: O = (96 - 4C) / 3
5. Substitute this O value into the 6C + O = 88 equation: 6C + (96 - 4C) / 3 = 88
6. Multiplying every term by 3 to eliminate the fraction: 18C + 96 - 4C = 264
7. Simplify to 14C = 168
8. Divide both sides by 14, C = 12 grams/mole for carbon
9. Using C in equation 1, 4(12) + 3O = 96
10. Simplify to 48 + 3O = 96
11. Subtract 48 from both sides, 3O = 48
12. Divide both sides by 3, O = 16 grams/mole for oxygen

So, the molar mass of carbon is 12 grams/mole and the molar mass of oxygen is 16 grams/mole.