Question

A 7.83 g sample of hcn contains 0.290 g of h and 4.06 g of n. find the mass of carbon in a sample of hcn with a mass of 3.37 g.

Answer 1

The mass of carbon in a 3.37 g sample of HCN, given the composition of a 7.83 g sample, is calculated by determining the mass percent of carbon from the original sample and applying it to the new sample's mass, resulting in approximately 1.497 g of carbon.

Step-by-step explanation:

To find the mass of carbon in a 3.37 g sample of HCN given the composition of a 7.83 g sample, we first need to establish the mass percentages of its components (hydrogen and nitrogen in this case) from the initial 7.83 g sample, which contains 0.290 g of hydrogen and 4.06 g of nitrogen. With these figures, we can determine the mass percentage of carbon in the sample by subtracting the mass of hydrogen and nitrogen from the total mass to find the mass of carbon in the original sample.

Mass of carbon in the original sample: 7.83 g (total mass) - 0.290 g (hydrogen) - 4.06 g (nitrogen) = 3.48 g (carbon).

Calculating the mass percent of carbon:
Mass percent of carbon = (3.48 g carbon / 7.83 g total sample) × 100 = 44.44%.

To find the mass of carbon in the new 3.37 g sample, we use the carbon mass percent:
Mass of carbon in the 3.37 g sample = 3.37 g (total sample) × 44.44% = 1.497 g.

Thus, the mass of carbon in a 3.37 g sample of HCN is approximately 1.497 g.

Answer 2

To obey the Law of Conservation of Mass, the sum of all individual elements of a compound is equal to the mass of the compound. So, if HCN has a mass of 7.83 grams, then

7.83 g = mass of H + mass of C + mass of N

We know the masses of H and N to be 0.290 g and 4.06 g, respectively. Hence, we can find for the mass of C:

7.83 = 0.29 + mass of C + 4.06
mass of C = 3.48 g

As an extension to the Law of Conservation of Mass, there is also a Law of Definite Proportions. According to Dalton's atomic theory, a compound is formed from a fixed ratio of its individual elements. From our previous calculations, we know that the mass ratio of H to C to N is 0.29 g: 3.48 g:4.06 grams. The ratio could also be expressed in percentages. Let's find the mass percentage of Carbon in HCN to be used later:

mass % of Carbon = (3.48 g/7.83 g)*100
mass % of Carbon = 44.44%

So, if you collect a different mass of HCN, say 3.37 g, the corresponding mass of Carbon is equal to:

Mass of Carbon = (3.37)(44.44%)
Mass of Carbon = 1.498 g