Methane gas contains carbon atoms and hydrogen atoms in the ratio of 1:4 . A sample of methane gas contains 90 atoms. What value should be inserted into each rectangle? (1 point) The number should be inserted into each rectangle.
The ratio of carbon atoms to hydrogen atoms in methane gas is 1:4, which means that for every 1 carbon atom, there are 4 hydrogen atoms.
Let's assume that the number of carbon atoms is x.
Therefore, the number of hydrogen atoms would be 4x, since for every carbon atom, there are 4 hydrogen atoms.
We know that the total number of atoms in the sample is 90.
So, we can write the equation:
x + 4x = 90
Simplifying the equation:
5x = 90
Dividing both sides by 5, we get:
x = 18
Therefore, the value that should be inserted into each rectangle is 18.
To find the value that should be inserted into each rectangle, we can set up a proportion based on the ratio of carbon atoms to hydrogen atoms.
The ratio of carbon atoms to hydrogen atoms is given as 1:4. This means that for every 1 carbon atom, there are 4 hydrogen atoms.
Let's assign x as the number of carbon atoms in the sample. Therefore, the number of hydrogen atoms would be 4x, as there are 4 hydrogen atoms for each carbon atom.
We know that the total number of atoms in the sample is 90. So, the expression for the total number of atoms can be written as x + 4x = 90.
Simplifying this equation, we get 5x = 90.
To find the value of x, we divide both sides of the equation by 5:
5x/5 = 90/5,
x = 18.
Therefore, the value that should be inserted into each rectangle is 18.
To solve this problem, we need to determine the number of carbon and hydrogen atoms in the sample of methane gas. Given that the ratio of carbon atoms to hydrogen atoms is 1:4, we can assume that the sample contains 1 part carbon and 4 parts hydrogen.
Let's find the number of carbon atoms first. We know that the ratio of carbon atoms to hydrogen atoms is 1:4, so the total ratio is 1+4=5. To find the number of carbon atoms, we divide the total number of atoms in the methane gas sample by the total ratio:
Total number of atoms / Total ratio = Number of carbon atoms
90 / 5 = 18
Therefore, the value that should be inserted into the rectangle for carbon atoms is 18.
To find the number of hydrogen atoms, we multiply the number of carbon atoms by the ratio of hydrogen atoms to carbon atoms:
Number of carbon atoms * Ratio of hydrogen atoms to carbon atoms = Number of hydrogen atoms
18 * 4 = 72
Therefore, the value that should be inserted into the rectangle for hydrogen atoms is 72.
In summary, the value 18 should be inserted into the rectangle for carbon atoms, and the value 72 should be inserted into the rectangle for hydrogen atoms.