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.

Solution

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In the first sample, we are given 7.83-g of HCN which contains 0.290 g of H and 4.06 g of N. On the second sample of HCN, we are required to find the mass of Carbon given that the sample has a mass of 3.37 g.


From the first sample, get the mass of the carbon atom for every 7.83-g of HCN sample.


We know that the mass of a substance is equal to the sum of the mass of its components

Let:

m= mass mHCN_{\text{HCN}}= mH_{\text{H}} + mC_{\text{C}} + mN_{\text{N}} 7.83 g= 0.290 g+ mC_{\text{C}} + 4.06 g 7.83 g- 0.290 g - 4.06 g=mC_{\text{C}} mC_{\text{C}}= 3.48 g Therefore for every 7.83 g of HCN, there are 3.48 g C. Or it can be written as 3.48 g C7.83g HCN\dfrac{3.48 \text{ g C}}{7.83 \text{g HCN}} From the second sample, we can now get the mass of carbon by the use of the ratio

3.37 g HCN×3.48 g C7.83g HCN=1.50\times \dfrac{3.48 \text{ g C}}{7.83 \text{g HCN}}=\boxed{1.50 } grams C

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