Need some help with these
1. A 15.0 carat (3.00g) diamond is found to be 99.9% carbon. What mass of carbon is in this diamond?
2. To make stainless steel, a metallurgist might “smelt” [melt and blend] together a 1250g iron “ingot” [bar], 1.500g of carbom and 200.0g of chromium. What is the full % composition of this “alloy” [metal mixture]?
1. 3.00 g x 0.999 = ?
2. %Fe = (g Fe/total weight)*100 = ?
%Cr = (g C/total weight)*100 = ?
%C = (g C/total weight)*100 = ?
Post your work if you get stuck.
Sure! I'd be happy to help you with those. Let's break down each question step by step.
1. To find the mass of carbon in the diamond, we need to calculate the mass of carbon in a 15.0 carat diamond that is 99.9% carbon.
First, convert 15.0 carats to grams. Since 1 carat is equal to 0.2 grams, convert 15.0 carats to grams by multiplying 15.0 carats by 0.2 grams/carat.
15.0 carats * 0.2 grams/carat = 3.00 grams
Now that we know the mass of the diamond is 3.00 grams, we can calculate the mass of carbon in the diamond by multiplying the mass of the diamond by the percentage of carbon.
3.00 grams * 0.999 (99.9% expressed as a decimal) = 2.997 grams
Therefore, the mass of carbon in the diamond is approximately 2.997 grams.
2. To find the full percentage composition of the alloy, we need to calculate the percentage of each element in the mixture (steel alloy).
First, add up the masses of iron, carbon, and chromium:
1250g + 1.500g + 200.0g = 1451.5g
Now, we can calculate the percentage composition of each element in the alloy.
Percentage of Iron = (mass of iron / total mass of alloy) * 100%
Percentage of Carbon = (mass of carbon / total mass of alloy) * 100%
Percentage of Chromium = (mass of chromium / total mass of alloy) * 100%
Calculating each percentage:
Percentage of Iron = (1250g / 1451.5g) * 100% ≈ 86.13%
Percentage of Carbon = (1.500g / 1451.5g) * 100% ≈ 0.10% (rounded to two decimal places)
Percentage of Chromium = (200.0g / 1451.5g) * 100% ≈ 13.77%
Therefore, the full percentage composition of the alloy is approximately 86.13% iron, 0.10% carbon, and 13.77% chromium.
I hope this helps! Let me know if you have any further questions.