Prepare 500ml of a 1:5 solution using a 1:10 solution and a 1:4 solution. What quantities will be used of each stock solution to make the 1:5 solution?
To prepare a 500ml 1:5 solution using a 1:10 solution and a 1:4 solution, we can use the following steps:
Step 1: Determine the desired final concentration:
The 1:5 solution means that there is 1 part of solute for every 5 parts of solution. In other words, the concentration is 1 part solute to 5 parts solution.
Step 2: Calculate the volume to be used for each stock solution:
Let's assume we will use x ml of the 1:10 solution and y ml of the 1:4 solution.
Step 3: Set up the equation for the concentration:
The total volume of the solution is 500 ml. So, the concentration equation can be written as:
(x ml of 1:10 solution) / (y ml of 1:4 solution) = 1/5
Step 4: Solve the equation for x and y:
To solve the equation, we need to set up another equation using the volume information. Since the total volume is 500 ml, we can write:
x ml + y ml = 500 ml
Step 5: Solve the system of equations:
Now we can solve the system of equations formed in step 4 and step 5 to find the values of x and y.
Using substitution or elimination method:
From equation 1:
x = (1/5)(y ml)
Substituting this value in equation 2:
(1/5)(y ml) + y ml = 500 ml
Simplifying:
y/5 + y = 500
(6/5)y = 500
y = (500 * 5)/6
y = 416.67 ml (approx.)
Substituting the value of y back into equation 1:
x = (1/5)(416.67 ml)
x = 83.33 ml (approx.)
Therefore, to prepare a 500ml 1:5 solution using a 1:10 solution and a 1:4 solution, you would need approximately 83.33 ml of the 1:10 solution and approximately 416.67 ml of the 1:4 solution.
To prepare a 500ml 1:5 solution using a 1:10 solution and a 1:4 solution, we need to determine the quantities required from each stock solution.
Let's take the following variables:
- Let x be the quantity (in ml) of the 1:10 solution needed.
- Let y be the quantity (in ml) of the 1:4 solution needed.
According to the given ratios, a 1:5 solution means that for every 1 part of the solute (or active ingredient), we need 5 parts of the total solution.
Now, let's set up the equation using the quantities and ratios:
For the 1:10 solution, the ratio is 1:10, which means for every 1 part of the solute, we have 10 parts of the solution. Therefore, the concentration of the solute in this solution is 1/10.
For the 1:4 solution, the ratio is 1:4, which means for every 1 part of the solute, we have 4 parts of the solution. Therefore, the concentration of the solute in this solution is 1/4.
We can calculate the total quantity of solute in the 500ml 1:5 solution by multiplying the desired 1:5 ratio by the final volume:
1/5 * 500ml = 100ml (this is the total quantity of solute needed in the 1:5 solution)
Since we have two unknowns (x and y), we need to set up another equation using the concentrations:
x * 1/10 + y * 1/4 = 100ml
Now, we can solve the above two equations simultaneously to find the values of x and y.
Hope this explanation helps! Let me know if you need further assistance.