Final answer:
To find the new molarity (M2) after dilution, use the dilution equation M1V1 = M2V2, convert all volumes to the same unit, and solve for M2. For example, a 2.0 M HCl solution diluted from 100 mL to 500 mL will have M2 = (2.0 M × 0.100 L) / 0.500 L resulting in a new molarity of 0.4 M.
Step-by-step explanation:
To find the final volume of water added to dilute a solution, we use the dilution equation M1 V1 = M2 V2 which represents the relationship between the molarity (M) and volume (V) of two different solutions, before and after dilution. To calculate the new molarity (M2), first, ensure that the volume units are consistent. For example, convert milliliters to liters if necessary, then solve for M2 by dividing both sides of the equation by V2.
Suppose we have 100 mL of a 2.0 M solution of HCl, which we dilute to a final volume of 500 mL. The initial molarity (M1) multiplied by the initial volume (V1) is equal to the final molarity (M2) multiplied by the final volume (V2). M2 is then calculated as follows:
M1 V1 = M2 V2
2.0 M × 0.100 L = M2 × 0.500 L
M2 = (2.0 M × 0.100 L) / 0.500 L
M2 = 0.4 M
The number of moles of solute remains the same after dilution, so by using the dilution equation we can also determine that the moles of solute before dilution (moles1) equals the moles after dilution (moles2), which means moles1 = M1 V1 and moles2 = M2 V2.