To find the percent by mass of each compound in the mixture, we need to determine the amount of NaCl and KCl present in the sample.
Let's break down the steps:
Step 1: Calculate the number of moles of AgCl produced.
Using the molar mass of AgCl (143 g/mol), we can determine the number of moles of AgCl produced.
Mass of AgCl = 1.822 g
Number of moles of AgCl = Mass of AgCl / Molar mass of AgCl = 1.822 g / 143 g/mol = 0.013 mol
Step 2: Write the chemical equation for the reaction.
The reaction between AgNO3 and the mixture of NaCl and KCl can be represented as follows:
2AgNO3 + NaCl -> AgCl + NaNO3
Step 3: Determine the moles of NaCl reacting with AgNO3.
From the balanced chemical equation mentioned above, we can see that 1 mole of NaCl reacts with 1 mole of AgCl.
Therefore, the number of moles of NaCl is also 0.013 mol.
Step 4: Set up an equation to determine the moles of KCl in the mixture.
Assuming x represents the moles of NaCl and y represents the moles of KCl, we can set up the following equation:
x/58 + y/74 = 0.013 mol
(Here, the molar mass of NaCl is 58 g/mol, and the molar mass of KCl is 74 g/mol.)
Simplifying this equation will give us:
0.0172x + 0.0134y = 0.013
Step 5: Determine the moles of KCl.
To solve the equation, we can substitute the given total mass of the mixture:
Total mass of mixture = mass of NaCl + mass of KCl = 0.887 g
We know that the mass of NaCl is x grams, so the mass of KCl will be (0.887 g - x grams).
Substituting the values, we'll have:
x/58 + (0.887-x)/74 = 0.013
Step 6: Solve the equation for x (NaCl) and y (KCl).
Solve the equation obtained in step 5 simultaneously to find the values of x (NaCl) and y (KCl).
Once you determine the values of x and y, you can calculate the percent by mass of each compound using the following formulas:
Percent by mass of NaCl = (mass of NaCl / total mass of mixture) * 100%
Percent by mass of KCl = (mass of KCl / total mass of mixture) * 100%