When 2.25 g of sodium hydroxide (NaOH) was dissolved in 150.00 g of water a value of 11.00oC was obtained for ΔT.
1. Calculate the molarity of the sodium hydroxide solution.
2. Calculate the value (calories) for the heat of solution of 2.25 g of NaOH.
3. Calculate the number of calories that would be produced if one mole of sodium hydroxide was dissolved. (ΔHsolnNaOH)
The process for #2 didn't work. I got found the answer to be -1590 but I'm not sure how to get that answer
1. Well, if you have 2.25 g of NaOH in a solution, you first need to convert that to moles. And given that the molar mass of NaOH is 40 g/mol, you divide 2.25 g by that to get 0.05625 mol.
Now, to calculate the molarity, you divide the number of moles of solute by the volume in liters. Since you're given the mass of water, you need to convert that to volume first. The density of water is approximately 1 g/mL, so 150.00 g of water is equal to 150.00 mL or 0.15000 L.
Finally, divide the number of moles (0.05625 mol) by the volume (0.15000 L), and you get the molarity of the sodium hydroxide solution. Math, math, math... turns out to be roughly 0.375 M.
2. To calculate the heat of solution, you need to use the formula q = m × C × ΔT, where q is the heat in calories, m is the mass in grams, C is the specific heat capacity (which is approximately 1 cal/g°C for water), and ΔT is the change in temperature.
So, plug in the numbers. We have 2.25 g for the mass, 1 cal/g°C for the specific heat capacity, and a ΔT of 11.00°C. Multiply those together, and you get your answer. It's... (wait for it...) approximately 24.75 calories!
3. Now, to calculate the number of calories for one mole of NaOH, first you need to find the number of moles in 2.25 g. We already did that earlier, it's 0.05625 mol.
Since 0.05625 mol of NaOH gives you 24.75 calories, you can set up a proportion using the molar ratio. One mole of NaOH is to 0.05625 mol as x calories is to 24.75 calories. Solve for x, and that gives you the number of calories produced if one mole of sodium hydroxide was dissolved. Pretty neat, huh?
To help answer the questions, we can use the equation:
ΔT = (Kf)(m)(i)
where:
ΔT = temperature change in °C
Kf = cryoscopic constant for water (1.86 °C/m)
m = molality of the solution
i = van 't Hoff factor (number of particles in the solute)
Let's break down each question step-by-step:
1. Calculate the molarity of the sodium hydroxide solution.
To find the molarity (M) of the sodium hydroxide solution, we need to find the moles of NaOH and the volume of the solution.
First, let's find the moles of NaOH:
moles of NaOH = mass of NaOH / molar mass of NaOH
The molar mass of NaOH is:
Na (22.99 g/mol) + O (16.00 g/mol) + H (1.01 g/mol) = 39.99 g/mol
moles of NaOH = 2.25 g / 39.99 g/mol = 0.0563 mol
Next, let's find the volume of the solution. Since we only have the mass of water, we need to assume that the density of the solution is 1 g/mL (since it's close to water).
volume of solution = mass of water / density of solution
volume of solution = 150.00 g / 1 g/mL = 150.00 mL
Now, let's convert the volume of the solution from mL to liters:
volume of solution = 150.00 mL * (1 L / 1000 mL) = 0.15000 L
Finally, we can calculate the molarity using the formula:
Molarity (M) = moles of solute / volume of solution in L
Molarity (M) = 0.0563 mol / 0.15000 L = 0.375 M
Therefore, the molarity of the sodium hydroxide solution is 0.375 M.
2. Calculate the value (calories) for the heat of solution of 2.25 g of NaOH.
To find the heat of solution, we can use the equation:
q = (ΔT)(ms)(s)
where:
q = heat of solution in calories
ΔT = temperature change in °C (given as 11.00 °C)
m = mass of solute in grams (given as 2.25 g)
s = specific heat capacity of water (1 cal/g°C)
q = (11.00 °C)(2.25 g)(1 cal/g°C) = 24.75 calories
Therefore, the value for the heat of solution of 2.25 g of NaOH is 24.75 calories.
3. Calculate the number of calories that would be produced if one mole of sodium hydroxide was dissolved. (ΔHsolnNaOH)
To find the number of calories produced when one mole of sodium hydroxide (NaOH) is dissolved, we can use a unit conversion.
We know that when 2.25 g of NaOH is dissolved, 24.75 calories are produced.
Now, let's convert grams to moles using the molar mass of NaOH:
moles of NaOH = 2.25 g / 39.99 g/mol = 0.0563 mol
Using a proportion, we can set up the conversion:
(24.75 calories) / (0.0563 mol) = x calories / (1 mol)
Solving for x, we get:
x = (24.75 calories) * (1 mol) / (0.0563 mol) = 439 calories
Therefore, the number of calories produced when one mole of sodium hydroxide is dissolved is 439 calories.
To answer these questions, we'll need to use the equation for heat of solution:
q = m * C * ΔT
Where:
q is the heat of solution (in calories)
m is the mass of the substance being dissolved (in grams)
C is the specific heat capacity of water (which is 1.00 cal/g°C)
ΔT is the change in temperature (in °C)
1. Calculate the molarity of the sodium hydroxide solution:
To find the molarity, we'll need to first calculate the moles of sodium hydroxide (NaOH) dissolved. We can use the formula:
moles = mass / molar mass
The molar mass of NaOH is 22.99 g/mol (sodium) + 16.00 g/mol (oxygen) + 1.01 g/mol (hydrogen) = 39.99 g/mol.
moles = 2.25 g / 39.99 g/mol = 0.0563 mol
Now, we can calculate the molarity using the formula:
molarity = moles / volume
We don't have the volume of the solution, but we know the mass of water (150.00 g). Assuming the density of water is 1.00 g/cm³, we can use the formula:
volume = mass / density
volume = 150.00 g / 1.00 g/cm³ = 150.00 cm³
Converting cm³ to liters:
volume = 150.00 cm³ * 1 L/1000 cm³ = 0.150 L
molarity = 0.0563 mol / 0.150 L = 0.375 M
So, the molarity of the sodium hydroxide solution is 0.375 M.
2. Calculate the value (calories) for the heat of solution of 2.25 g of NaOH:
We'll use the formula mentioned at the beginning:
q = m * C * ΔT
Substituting the values:
q = 2.25 g * 1.00 cal/g°C * 11.00°C = 24.75 cal
Therefore, the heat of solution of 2.25 g of NaOH is 24.75 calories.
3. Calculate the number of calories that would be produced if one mole of sodium hydroxide was dissolved (ΔHsolnNaOH):
Since we know the heat of solution of 2.25 g of NaOH (24.75 cal), we can use this to calculate the heat of solution for one mole.
ΔHsolnNaOH = q / moles
ΔHsolnNaOH = 24.75 cal / 0.0563 mol = 439 cal/mol
Therefore, the number of calories produced when one mole of sodium hydroxide is dissolved is 439 calories (ΔHsolnNaOH).
1. mols NaOH = grams/molar mass
Then M = mols/L solution. I suppose you are supposed to take the density of H2O as 1.0 g/mL which makes 150.00g H2O= 150 mL.
2. q = mass H2O x specific heat H2O x delta T
3. delta H rxn = q/2.25 give you per gram.
That x molar mass NaOH gives delta H rxn per mole.