a certain molecule contains twice as many atoms of hydrogen as oxygen and one more atom of carbon than hydrogen. If there are 21 atoms altogether in the molecule, how many atoms of carbon are there?
Well, well, well, looks like we've got a molecular investigation on our hands! Let me put on my lab coat and calculate this for you.
Let's assume the number of oxygen atoms is "x." According to the information given, we know that the number of hydrogen atoms is twice that of oxygen atoms, so we have 2x hydrogen atoms. And adding up all the atoms, including carbon, gives us a total of 21: x + 2x + (2x + 1) = 21.
Now, let's do a little math magic here. Combining like terms, we get 5x + 1 = 21. Subtracting 1 from both sides, we're left with 5x = 20. Next, we divide both sides by 5, giving us X = 4.
So, there are 4 oxygen atoms, meaning there are twice as many hydrogen atoms, which would be 8. And finally, since there's one more atom of carbon than hydrogen, we add 1 to 8 to find that there are... drumroll, please... 9 atoms of carbon!
Ta-da! Case closed, molecule solved!
Let's solve this step by step.
Let's assume the number of oxygen atoms is "x".
According to the information given,
- The number of hydrogen atoms is twice as many as oxygen atoms, so it will be 2*x.
- The number of carbon atoms is one more than the number of hydrogen atoms, so it will be 2*x + 1.
The total number of atoms in the molecule is given as 21.
So, the equation can be written as:
x + 2*x + 2*x + 1 = 21
Combining like terms, we get:
5*x + 1 = 21
Subtracting 1 from both sides of the equation, we get:
5*x = 20
Dividing both sides by 5, we get:
x = 4
So, the number of carbon atoms is 2*x + 1, which is:
2*4 + 1 = 9
Therefore, there are 9 atoms of carbon in the molecule.
To find the number of atoms of carbon in the molecule, we need to analyze the information provided about the ratios of hydrogen, oxygen, and carbon.
Let's assign variables to the unknown quantities:
Let H represent the number of hydrogen atoms.
Let O represent the number of oxygen atoms.
Let C represent the number of carbon atoms.
From the given information, we can deduce two equations:
1) The molecule contains twice as many atoms of hydrogen as oxygen:
H = 2O
2) The molecule contains one more atom of carbon than hydrogen:
C = H + 1
We also know that the total number of atoms in the molecule is 21:
H + O + C = 21
Now, we will use these equations to solve for the number of atoms of carbon (C).
Substitute equation 1) into equation 2):
C = 2O + 1 + 1
C = 2O + 2
Substitute these expressions into equation 3):
2O + 2 + O + (2O + 2) = 21
5O + 4 = 21
5O = 21 - 4
5O = 17
O = 17/5
O ≈ 3.4
Since the number of atoms must be a whole number, we round down to the nearest whole number:
O = 3
Substitute this value of O into equation 1):
H = 2O
H = 2(3)
H = 6
Substitute the values of H and O into equation 3):
6 + 3 + C = 21
9 + C = 21
C = 21 - 9
C = 12
Therefore, the number of atoms of carbon in the molecule is 12.