How many litres nitric acid 70% w/w and how many litres of water do I need to prepare a 47 v% nitric acid solution. Please help.
To determine the amount of nitric acid (70% w/w) and water needed to prepare a 47% v/v nitric acid solution, we can use the equation:
(Volume of Nitric Acid × % Nitric Acid) + (Volume of Water × % Water) = Total Volume × Target % Nitric Acid
Let's calculate this step-by-step:
Step 1: Convert the given concentrations to decimal form:
70% w/w nitric acid can be converted to 0.7 concentration of nitric acid (since w/w refers to weight/weight).
47% v/v nitric acid can be directly converted to 0.47 concentration of nitric acid (since v/v refers to volume/volume).
Step 2: Assign variables:
Let 'x' represent the volume of nitric acid (in liters) and 'y' represent the volume of water (in liters) needed.
Step 3: Using the equation:
(x × 0.7) + (y × 0) = (x + y) × 0.47
Since water does not contain nitric acid, its percentage is 0%.
With this equation, we can simplify it to:
0.7x = 0.47(x + y)
Step 4: Solve for 'y':
0.7x = 0.47x + 0.47y
0.7x - 0.47x = 0.47y
0.23x = 0.47y
y = (0.23x) / 0.47
So, the volume of water 'y' can be represented as:
y = (0.23x) / 0.47
Step 5: Substitute this value of 'y' in terms of 'x' back into the equation to solve for 'x'.
(x × 0.7) + ((0.23x) / 0.47) × 0 = (x + ((0.23x) / 0.47)) × 0.47
Now you can solve for 'x' using algebraic methods or numerical methods like substitution, elimination, or using software such as Excel or a scientific calculator to find the value of 'x'.