A 58.44-g sample of sodium chloride contains 35.45 g of chlorine, with sodium being the only other element. How many grams of sodium are in a sample of 13.74 g of sodium chloride?
The ratio of sodium to total mass is constant, so
x/13.74 = (58.44-35.45)/58.44
I want to point out that I don't like the way the problem is stated. The sample contains 35.45 g Cl or 35.45 g chloride but not 35.45 g chloRINE. This is a common error made by students and teachers alike. I have seen it in texts, also but that doesn't make it any more correct.
To find the amount of sodium (Na) in a sample of sodium chloride (NaCl), we can use the information provided.
Given that the sample of sodium chloride has a mass of 58.44 g and contains 35.45 g of chlorine (Cl), we can find the amount of sodium by subtracting the mass of chlorine from the total mass of the sample.
Mass of sodium chloride (NaCl) = 58.44 g
Mass of chlorine (Cl) = 35.45 g
Mass of sodium (Na) = Mass of sodium chloride - Mass of chlorine
Mass of sodium (Na) = 58.44 g - 35.45 g
Mass of sodium (Na) = 22.99 g
Therefore, a sample of 13.74 g of sodium chloride would contain 22.99 g of sodium.
To find the grams of sodium in a sample of sodium chloride, we need to use the information given about the relative masses of sodium and chlorine.
1. Start by calculating the percentage of chlorine in sodium chloride:
Percentage of chlorine = (mass of chlorine / mass of sodium chloride) × 100
Given that the mass of chlorine is 35.45 g and the mass of sodium chloride is 58.44 g:
Percentage of chlorine = (35.45 g / 58.44 g) × 100
2. Determine the percentage of sodium in sodium chloride by subtracting the percentage of chlorine from 100:
Percentage of sodium = 100% - Percentage of chlorine
3. Calculate the grams of sodium in a 13.74 g sample of sodium chloride:
Grams of sodium = (mass of sodium chloride / 100) × Percentage of sodium
Given that the mass of sodium chloride is 13.74 g:
Grams of sodium = (13.74 g / 100) × Percentage of sodium
Plug in the values to calculate the grams of sodium:
Percentage of chlorine = (35.45 g / 58.44 g) × 100
Percentage of sodium = 100% - Percentage of chlorine
Grams of sodium = (13.74 g / 100) × Percentage of sodium
After performing the calculations, you will find the answer to be the grams of sodium in a sample of 13.74 g of sodium chloride.