Preparing a 20% Sucrose Solution from 750g of Sucrose and Water
To prepare a 20% solution of sucrose, you need to ensure that the mass of sucrose is 20% of the total mass of the solution. This article will guide you through the mathematical calculation and steps necessary to achieve this concentration.
Mathematical Calculation
Let's denote the mass of water to be added as m. The total mass of the solution is the sum of the mass of sucrose and the mass of water:
Total mass of solution u2192 750g sucrose mg water
The formula for the percentage of a solution is given by:
Percentage u2192 (mass of solute / total mass of solution) * 100
In this case, we want the percentage to be 20:
20 u2192 (750 / (750 m)) * 100
Solving for the Mass of Water
Rearranging the equation to solve for m:
0.20 u2192 750 / (750 m)
Cross-multiplying:
0.20 * (750 m) u2192 750
Distributing:
150 0.20*m u2192 750
Subtracting 150 from both sides:
0.20*m u2192 600
Dividing by 0.20:
m u2192 600 / 0.20 u2192 3000 g
Therefore, the mass of water necessary to add is 3000 grams.
Alternative Calculation Methods
Another approach involves using the formula:
20 u2192 (750 / x) * 100
Solving for x:
0.20 * x u2192 750
x u2192 750 / 0.20 u2192 3750 g H2O
This confirms that 3000 grams of water is required to achieve a 20% sucrose solution.
Simultaneous Equations Approach
Based on the given information, we can set up the following simultaneous equations:
X Y u2192 750 (initial mass)
X / (750 - Y) u2192 0.20 (final concentration)
Solving these equations:
Y u2192 500 g water
X u2192 250 g solute
And to achieve the desired concentration, we need to add 500 grams of water.
Confirmation of Initial Calculations
By substituting back the values, we can confirm the initial calculations:
Total mass 750g (sucrose) 3000g (water) u2192 3750g
20% solution u2192 (750 / 3750) * 100 u2192 20%
This process ensures that you have accurately prepared the desired 20% sucrose solution.
Final Thoughts
The key to preparing a 20% sucrose solution is ensuring that the mass of sucrose is 20% of the total mass of the solution. By carefully calculating the mass of water needed, we can achieve the desired concentration accurately. Whether using basic algebraic methods or simultaneous equations, the approach remains the same, emphasizing accuracy and precision in solution preparation.