A solution that is formed by combining 400. mL of 0.20 M HNO3 with 600. mL of 0.10 M NaOH has an H3O+ concentration of
a. 0.20 M.
b. 0.10 M.
c. 0.060 M.
d. 0.020 M.
e. 5.0 ´ 10-13.
c. 0.060 M.
To determine the H3O+ concentration of the solution formed by combining HNO3 and NaOH, we need to use the concept of neutralization.
The balanced equation for the neutralization reaction between HNO3 and NaOH is:
HNO3 + NaOH → NaNO3 + H2O
From the balanced equation, we can see that the same number of moles of H+ ions from HNO3 and OH- ions from NaOH react to form H2O. Therefore, in the resulting solution, all the HNO3 and NaOH react completely to form water and sodium nitrate (NaNO3) without any leftover H+ or OH- ions.
This means that the resulting solution will be neutral, so the H3O+ concentration will be equal to the OH- concentration, which can be calculated using the concept of dilution.
First, let's calculate the moles of HNO3 and NaOH in the given volumes:
Moles of HNO3 = (Volume of HNO3) × (Concentration of HNO3)
= 0.400 L × 0.20 mol/L
= 0.080 mol
Moles of NaOH = (Volume of NaOH) × (Concentration of NaOH)
= 0.600 L × 0.10 mol/L
= 0.060 mol
Since the balanced equation shows that 1 mole of HNO3 reacts with 1 mole of NaOH, we can see that the limiting reactant is NaOH because it has fewer moles than HNO3.
Therefore, all of the 0.060 moles of NaOH will react with 0.060 moles of HNO3 to form water and NaNO3.
This means that there will be no excess HNO3 remaining in the solution. Thus, there will be no excess H+ ions in the resulting solution.
As a result, the H3O+ concentration of the solution formed will be 0 M, which is not listed as an option.
Therefore, the correct answer is none of the given options.
To find the H3O+ concentration in the solution formed by combining HNO3 and NaOH, we need to determine the moles of HNO3 and NaOH, and then use stoichiometry to calculate the concentration of H3O+.
Step 1: Calculate the moles of HNO3 used.
The volume of HNO3 used is 400. mL, and the concentration is 0.20 M.
Using the formula: moles = volume (L) x concentration (M),
we convert the volume to liters: 400. mL = 0.4 L,
Now, we calculate the moles of HNO3: moles = 0.4 L x 0.20 M = 0.08 moles.
Step 2: Calculate the moles of NaOH used.
The volume of NaOH used is 600. mL, and the concentration is 0.10 M.
Using the same formula: moles = volume (L) x concentration (M),
we convert the volume to liters: 600. mL = 0.6 L,
Now, we calculate the moles of NaOH: moles = 0.6 L x 0.10 M = 0.06 moles.
Step 3: Use stoichiometry to determine the moles of H3O+ formed.
The equation for the reaction between HNO3 and NaOH is:
HNO3 + NaOH → NaNO3 + H2O
From the balanced equation, we can see that for every 1 mole of HNO3, 1 mole of H3O+ is formed.
So, the moles of H3O+ formed is equal to the moles of HNO3 used, which is 0.08 moles.
Step 4: Calculate the concentration of H3O+ in the solution.
To calculate the concentration, we need the final volume of the solution.
The total volume of the solution is the sum of the volumes of HNO3 and NaOH used: 400. mL + 600. mL = 1000. mL = 1.0 L.
Now we divide the moles of H3O+ (0.08 moles) by the volume of the solution (1.0 L):
concentration = moles / volume = 0.08 moles / 1.0 L = 0.08 M.
Therefore, the H3O+ concentration in the solution is 0.08 M.
None of the given answer choices match this result, so the correct answer is not provided.