How many mL of a 4.7 M HNO3(aq) solution are required to make 500 mL of a solution with pH=2.10
Convert pH of 2.10 to (H^+) which is the same as (HNO3) since HNO3 is 100% ionized. Then the dilution formula is
c1v1 = c2v2
8.45E-4
To determine the mL of a 4.7 M HNO3 solution required to make a solution with pH 2.10, we need to consider the relationship between pH, concentration, and volume.
Step 1: Understand the problem:
pH is a measure of the acidity or alkalinity of a solution and is defined as the negative logarithm (base 10) of the hydrogen ion concentration ([H+]) in moles per liter (mol/L). The lower the pH value, the more acidic the solution.
Concentration is the amount of solute (in this case, HNO3) dissolved in a given amount of solvent (water) and is usually expressed in moles per liter (mol/L).
Volume is the amount of solution in liters (L) or milliliters (mL).
Step 2: Convert pH to [H+] concentration:
pH values can be converted to [H+] concentration using the equation:
[H+] = 10^(-pH)
Substituting the given pH value:
[H+] = 10^(-2.10) = 0.007943 mol/L
Step 3: Determine the required moles of HNO3:
The concentration of the 4.7 M HNO3 solution means that 4.7 moles of HNO3 are dissolved in 1 L (1000 mL) of solution.
So, the number of moles required can be calculated as follows:
moles of HNO3 = [H+] concentration * volume of solution (in L)
Since the volume of the solution is given as 500 mL, we need to convert it to liters:
volume of solution (in L) = 500 mL / 1000 mL/L = 0.5 L
Now, substitute the values to calculate the required moles of HNO3:
moles of HNO3 = 0.007943 mol/L * 0.5 L = 0.0039715 mol
Step 4: Calculate the required mL of 4.7 M HNO3:
Since the original solution is 4.7 M, it means that 4.7 moles of HNO3 are present in 1 L (1000 mL) of the solution.
To determine the required mL of the 4.7 M HNO3 solution, we divide the moles required (0.0039715 mol) by the concentration (4.7 M) and multiply by 1000 mL/L to convert to mL:
mL of 4.7 M HNO3 solution = (0.0039715 mol / 4.7 mol/L) * 1000 mL/L = 0.846 mL
Therefore, approximately 0.846 mL of the 4.7 M HNO3 solution is required to make 500 mL of a solution with pH 2.10.