Question

A sample of chemical X is found to contain 5.0 grams of oxygen, 10.0 grams of carbon, and 20.0 grams of nitrogen. The law of definite proportion would predict that a 75 gram sample of chemical X should contain how many grams of carbon

Answer 1

Answer: 75 grams sample of chemical X should contain 21.43 grams of carbon

Explanation: The law of definite proportion states that a given chemical compound always contains its component elements in fixed ratio.

From the question, chemical X contains 5.0 grams of oxygen, 10.0 grams of carbon, and 20.0 grams of nitrogen.

Sum up the masses

5.0g + 10.0g + 20.0g = 35.0g

This means, 10.0 grams of carbon are present in 35.0 grams of chemical X.

Now, to the determine the mass of carbon that 75 gram sample of chemical X should contain,

According to the law of definite proportion, the component elements of a given chemical compound are in fixed ratio. Therefore,

If 35.0g of chemical X contains 10.0g of carbon

Then, 75 g of chemical X will contain

(75 × 10) / 35 g

= 21.43 grams

Hence, 75 grams sample of chemical X should contain 21.43 grams of carbon.

Answer 2

Answer:

According to the law of definite proportion, a 75 gram sample of chemical X should contain 21.249 grams of carbon.

Explanation:

The total mass of the sample is equal to the sum of masses of oxygen, carbon and nitrogen. That is:

$m_{tot} = m_{O} + m_{C} + m_{N}$

If $m_{O} = 5\,g$, $m_{C} = 10\,g$ and $m_{N} = 20\,g$, then:

$m_{tot} = 35\,g$

According to the law of definite proportion, the following simple rule of three is used:

$m_{C'} = m_{C} \times \frac{m_{tot'}}{m_{tot}}$

If $m_{C} = 10\,g$, $m_{tot} = 35\,g$ and $m_{tot'} = 75\,g$, then:

$m_{C'} = 10\,g\times \frac{75\,g}{35\,g}$

$m_{C'} = 21.429\,g$

According to the law of definite proportion, a 75 gram sample of chemical X should contain 21.249 grams of carbon.