Calculate the amount of water (in grams) that must be added to (a)5.00 g of urea (NH2)2CO in the preparation of a 16.2 percent by mass solution, and (b)26.2g of MgCl2 in the preparation of a 1.5 percent by mass solution.
To calculate the amount of water that must be added to each solution, we need to use the formula for mass percent composition:
Mass percent = (mass of solute / total mass of solution) x 100
Let's begin with part (a) and calculate the amount of water needed for the urea solution.
(a) Urea Solution:
Given:
Mass of urea solute (NH2)2CO = 5.00 g
Mass percent composition = 16.2%
Step 1: Calculate the total mass of the solution.
Let's assume the total mass of the solution is M grams.
Step 2: Calculate the mass of urea in the solution.
Using the mass percent composition formula:
Mass of urea = (mass percent / 100) x total mass
5.00 g = (16.2 / 100) x M
5.00 g = 0.162M
M = 5.00 g / 0.162
M ≈ 30.85 g
Step 3: Calculate the mass of water in the solution.
Mass of water = Total mass - Mass of urea
Mass of water = 30.85 g - 5.00 g
Mass of water ≈ 25.85 g
Therefore, approximately 25.85 grams of water must be added to 5.00 g of urea to prepare a 16.2% by mass solution.
(b) Magnesium Chloride (MgCl2) Solution:
Given:
Mass of MgCl2 solute = 26.2 g
Mass percent composition = 1.5%
Step 1: Calculate the total mass of the solution.
Let's assume the total mass of the solution is N grams.
Step 2: Calculate the mass of MgCl2 in the solution.
Using the mass percent composition formula:
Mass of MgCl2 = (mass percent / 100) x total mass
26.2 g = (1.5 / 100) x N
26.2 g = 0.015N
N = 26.2 g / 0.015
N ≈ 1746.67 g
Step 3: Calculate the mass of water in the solution.
Mass of water = Total mass - Mass of MgCl2
Mass of water = 1746.67 g - 26.2 g
Mass of water ≈ 1720.47 g
Therefore, approximately 1720.47 grams of water must be added to 26.2 g of MgCl2 to prepare a 1.5% by mass solution.
To calculate the amount of water that must be added to a given amount of solute in order to prepare a solution of a specific percent by mass, you need to follow a few steps.
(a) For the first question, let's calculate the amount of water that must be added to 5.00 g of urea (NH2)2CO in order to prepare a 16.2 percent by mass solution.
Step 1: Find the mass of the solute:
Given that the mass of urea is 5.00 g.
Step 2: Calculate the mass of the solution:
The percent by mass is given as 16.2%, which means that the solute's mass is 16.2% of the total mass of the solution. Therefore, the mass of the solution is given by the equation:
mass of solution = (mass of solute) / (percent by mass)
mass of solution = 5.00 g / (16.2/100) = 30.86 g
Step 3: Calculate the mass of water:
The mass of the water can be determined by subtracting the mass of the solute from the mass of the solution.
mass of water = mass of solution - mass of solute
mass of water = 30.86 g - 5.00 g = 25.86 g
Therefore, you need to add 25.86 grams of water to 5.00 grams of urea to prepare a 16.2 percent by mass solution.
(b) Now, let's calculate the amount of water that must be added to 26.2 g of MgCl2 in order to prepare a 1.5 percent by mass solution.
Step 1: Find the mass of the solute:
Given that the mass of MgCl2 is 26.2 g.
Step 2: Calculate the mass of the solution:
The percent by mass is given as 1.5%, which means that the solute's mass is 1.5% of the total mass of the solution. Therefore, the mass of the solution is given by the equation:
mass of solution = (mass of solute) / (percent by mass)
mass of solution = 26.2 g / (1.5/100) = 1746.67 g
Step 3: Calculate the mass of water:
The mass of the water can be determined by subtracting the mass of the solute from the mass of the solution.
mass of water = mass of solution - mass of solute
mass of water = 1746.67 g - 26.2 g = 1720.47 g
Therefore, you need to add 1720.47 grams of water to 26.2 grams of MgCl2 to prepare a 1.5 percent by mass solution.
a)
[5.00/(5+x)] = 0.162
Solve for x.