thank you for any help possible.
Given a Mass Percent 13.3% and a Mass Solvent of 325.2 g, find Mass of Solute and Mass of Solution.
Mass%=13.3%
Mass solvent= 325.2g
solve for the Mass solute and Mass solution. This is all the information I am given.
mass% = [(g solute/g solute + g solvent)]*100
Let x = grams solute
13.3 = 100*(x/x + 325.2)
Solve for x = g solute.
To solve this problem, we need to understand what the mass percent represents. The mass percent is a measure of the concentration of a solution and is defined as the mass of the solute divided by the mass of the solution, multiplied by 100%. In your case, the mass percent is given as 13.3%.
Let's use the following variables:
- Mass solute (m_solute): This represents the mass of the solute.
- Mass solution (m_solution): This represents the mass of the entire solution, which includes both the solvent and the solute.
- Mass solvent (m_solvent): This represents the mass of the solvent.
Given information:
- Mass solvent (m_solvent) = 325.2 g
- Mass percent (%) = 13.3%
We need to find the mass of the solute (m_solute) and the mass of the solution (m_solution).
Step 1: Calculate the mass of the solute (m_solute) using the mass percent formula.
Mass percent formula:
Mass percent (%) = (Mass solute / Mass solution) × 100%
Rearranging the formula to solve for Mass solute:
Mass solute = (Mass percent / 100%) × Mass solution
Substituting the given values:
Mass solute = (13.3% / 100%) × Mass solution
Step 2: Calculate the mass of the solution (m_solution).
The mass of the solution (m_solution) is the sum of the mass of the solvent (m_solvent) and the mass of the solute (m_solute).
m_solution = m_solvent + m_solute
Substituting the given values:
m_solution = 325.2 g + Mass solute
Now, let's calculate the values.
Step 1 (Continued):
Mass solute = (13.3% / 100%) × Mass solution
Mass solute = (13.3 / 100) × Mass solution [Converting percentage to decimal]
Step 2 (Continued):
m_solution = 325.2 g + Mass solute
Now, we have two equations. Let's solve them simultaneously to find the values of Mass solute and Mass solution.
Mass solute = (13.3 / 100) × (325.2 g + Mass solute)
Expanding the equation:
Mass solute = (13.3 / 100) × 325.2 g + (13.3 / 100) × Mass solute
Rearranging the equation to isolate the Mass solute term:
Mass solute - (13.3 / 100) × Mass solute = (13.3 / 100) × 325.2 g
Combining like terms:
Mass solute × (1 - 13.3 / 100) = (13.3 / 100) × 325.2 g
Calculating the fraction:
Mass solute × (100 - 13.3) / 100 = (13.3 / 100) × 325.2 g
Simplifying:
Mass solute × 86.7 / 100 = 43.23636 g
Dividing by 86.7 / 100:
Mass solute = 43.23636 g / (86.7 / 100)
Mass solute = 49.896208 g
Now, let's substitute the found Mass solute value into the equation to calculate Mass solution.
m_solution = 325.2 g + Mass solute
m_solution = 325.2 g + 49.896208 g
m_solution = 375.096208 g
Therefore, the Mass solute is 49.896208 g and the Mass solution is 375.096208 g.