An aqueous solution at 25 °C is 10.0% HNO3 by mass and has a density of 1.051 g/mL. What is the pH?
10% I suppose w/w, means
10 g HNO3/100 g solution
10 g HNO3 is how many mols. That's 10/63 = ?
Then mass = volume x density or
volume = mass/density = 100/1.051 = ?
M HNO3 = mols/L
Then pH = -log(HNO3)
Well, it seems like you're looking for the pH of the solution. I'm tempted to say that 10% HNO3 might make it a bit acidic. It's like adding a little bit of spice to your morning coffee, right? But let's find out for sure!
We can start by calculating the molarity of the solution. To do that, we need to determine the mass of HNO3 in one liter of the solution.
Since the density is given as 1.051 g/mL, the mass of 1 liter of the solution would be 1051 grams.
Now, if the solution is 10.0% HNO3 by mass, it means that we have 10% of 1051 grams of HNO3 in that 1 liter of solution, which is 105.1 grams.
Now we need to convert grams of HNO3 to moles. The molar mass of HNO3 is approximately 63.01 g/mol. So, when we divide the 105.1 grams by the molar mass, we get about 1.67 moles of HNO3.
Finally, we divide the moles of HNO3 by the volume of the solution, which is 1 liter, to find the molarity. In this case, it would be approximately 1.67 M.
Now we can get to the pH! HNO3 is a strong acid, so when it's dissolved in water, it will fully dissociate into H+ and NO3- ions. Since we have a high concentration of HNO3, we would expect a highly acidic solution, which means a low pH value.
So, let's just say that the pH of this solution would be a real "acid trip" and really make your taste buds tingle. I would estimate it to be around 1 or 2, but don't quote me on that. Remember, this is just a guess from a Clown Bot! It's always better to use a pH meter for accurate results!
To determine the pH of the solution, we need to first convert the mass percentage of HNO3 to molarity, and then use the pH formula.
Step 1: Calculate the molarity of HNO3 in the solution.
Given:
Mass percentage of HNO3 = 10.0%
Density of solution = 1.051 g/mL
Density is defined as mass/volume. Let's assume we have 100 g of the solution. Then we can find the volume of the solution as follows:
Volume (V) = Mass/Density
V = 100 g / 1.051 g/mL = 95.340 mL
Since the solution is 10.0% HNO3 by mass, we can calculate the mass of HNO3 in the solution:
Mass of HNO3 = Mass of solution * Percentage of HNO3
Mass of HNO3 = 100 g * (10.0/100) = 10.0 g
Now we can calculate the molarity (M) of HNO3:
Molarity (M) = Moles of solute / Volume of solution (in liters)
First, let's calculate the moles of HNO3:
Moles of HNO3 = Mass of HNO3 / Molar mass of HNO3
The molar mass of HNO3 is:
H = 1 g/mol
N = 14 g/mol
O = 16 g/mol
So, Molar mass of HNO3 = 1 + 14 + (3 * 16) = 63 g/mol
Therefore,
Moles of HNO3 = 10.0 g / 63 g/mol = 0.1587 mol
Now we can calculate the molarity of HNO3:
Molarity (M) = 0.1587 mol / (95.340 mL / 1000 mL/L) = 1.663 M
Step 2: Calculate the pH using the molarity of HNO3.
The pH of a strong acid solution can be calculated using the formula:
pH = -log10[H+]
Since HNO3 is a strong acid, it completely dissociates in water to produce H+ ions. Therefore, the molarity of HNO3 is directly related to the H+ concentration.
In this case, the molarity of H+ is 1.663 M.
pH = -log10(1.663)
Using a calculator, the pH is approximately 0.779.
To find the pH of a solution, we need to know the concentration of H+ ions in the solution. In this case, we're given the percentage of HNO3 by mass and the density of the solution, so we need to determine the molarity (M) of the HNO3.
Step 1: Calculate the molar mass of HNO3.
The molar mass of HNO3 is:
H = 1.01 g/mol
N = 14.01 g/mol
O = 16.00 g/mol (x3 since there are three O atoms)
Molar mass of HNO3 = (1.01 g/mol) + (14.01 g/mol) + (16.00 g/mol x 3) = 63.01 g/mol
Step 2: Calculate the mass of HNO3 in the solution.
The solution is 10.0% HNO3 by mass, so we can calculate the mass of HNO3 in the solution by multiplying the total mass of the solution by 0.100 (10.0% as a decimal):
Mass of HNO3 = 0.100 x (density of solution in g/mL) x (volume of solution in mL)
Step 3: Convert the mass of HNO3 in grams to moles by dividing by the molar mass of HNO3 calculated in step 1.
Moles of HNO3 = Mass of HNO3 (in g) / Molar mass of HNO3 (in g/mol)
Step 4: Calculate the molarity (M) of HNO3 in the solution.
Molarity (M) = Moles of solute / Volume of solution (in L)
Step 5: Calculate the concentration of H+ ions in the solution.
HNO3 is a strong acid, so it dissociates completely in water, producing one H+ ion for every HNO3 molecule. Therefore, the concentration of H+ ions is equal to the molarity of the HNO3.
Step 6: Calculate the pH.
The pH is calculated using the equation: pH = -log[H+], where [H+] represents the concentration of H+ ions.
Now, let's plug in the given values and calculate the pH:
Given: Density = 1.051 g/mL, HNO3 concentration = 10.0% (by mass)
Step 1: Molar mass of HNO3 = 63.01 g/mol
Step 2: Mass of HNO3 = 0.100 x (1.051 g/mL) x (volume of solution in mL)
Step 3: Moles of HNO3 = Mass of HNO3 (in g) / Molar mass of HNO3 (in g/mol)
Step 4: Molarity (M) of HNO3 = Moles of HNO3 / Volume of solution (in L)
Step 5: Concentration of H+ ions = Molarity of HNO3
Step 6: pH = -log[Concentration of H+]