an aqueous solution solution of sodium borate is sometimes used to to fire-proof wood.
a. what is the molarity of 2.50 L of solution that contains 1.85 moles of sodium borate?
b. what is the molarity of 45.0 L of solution that contains 6.78 kg of sodium borate?
c. how manny moles of sodium borate are in 600.0 mL of a 1.57 M sodium borate solution?
d. a chemist needs 50.8 g of sodium borste for a reaction. How many mL of 1.87 M solution contain this mass?
An aqueous solution solution of sodium borate is sometimes used to to fire-proof wood.
a. what is the molarity of 2.50 L of solution that contains 1.85 moles of sodium borate?
M = mols/L
b. what is the molarity of 45.0 L of solution that contains 6.78 kg of sodium borate?
Convert kg to grams, then
mols sodium borate = grams/molar mass.
Then M = mols/L
c. how many moles of sodium borate are in 600.0 mL of a 1.57 M sodium borate solution?
mols = M x L
d. a chemist needs 50.8 g of sodium borste for a reaction. How many mL of 1.87 M solution contain this mass?
How many mols do you need? That's mols = grams/molar mass. solve for mols. Then
M = mols/L; rearrange to L = mols/M. You have mol and M, solve for L and convert to mL.
a. Well, if you have 1.85 moles of sodium borate in 2.50 L of solution, the molarity can be calculated using the formula Molarity = moles/volume. So, the molarity would be 1.85 moles/2.50 L = 0.74 M. Now, that's some serious "morality"!
b. Now, if you have 6.78 kg of sodium borate in 45.0 L of solution, you first need to convert the mass to moles. The molar mass of sodium borate is about 61.83 g/mol. So, the number of moles is 6.78 kg / (61.83 g/mol) = 109.99 moles. Now, divide this by the volume, giving a molarity of 109.99 moles/45.0 L ≈ 2.44 M. That's quite a concentrated solution – it's like sodium borate on steroids!
c. To find the number of moles of sodium borate in 600.0 mL of a 1.57 M sodium borate solution, you can use the formula Moles = Molarity x Volume. Plugging in the values, you get 1.57 M x 0.600 L = 0.942 moles of sodium borate. That's a whole mole-ful amount of fun!
d. If you need 50.8 g of sodium borate and you have a 1.87 M solution, you can use the formula Moles = Mass/Molar mass to find the number of moles. In this case, the molar mass of sodium borate is again 61.83 g/mol. So, the moles would be 50.8 g / 61.83 g/mol = 0.82 moles. Now, using the formula Moles = Molarity x Volume, you can rearrange to find the volume: Volume = Moles / Molarity. Plugging in the values, you have 0.82 moles / 1.87 M = 0.44 L, or 440 mL. So, you'll need 440 mL of that solution. Just don't get tangled up in those molarity calculations – it could make you lament sodium borate!
To solve these problems, we will use the formula:
Molarity (M) = moles of solute / volume of solution in liters
a. To find the molarity of 2.50 L of solution containing 1.85 moles of sodium borate:
Molarity (M) = 1.85 moles / 2.50 L
Molarity = 0.74 M
b. To find the molarity of 45.0 L of solution containing 6.78 kg of sodium borate:
First, we need to convert the mass of sodium borate from kilograms to grams:
6.78 kg = 6780 g
Next, we need to convert grams to moles by dividing by the molar mass of sodium borate:
Molar mass of sodium borate (Na2B4O7) = 22.99 g/mol (2 sodium atoms) + 10.81 g/mol (4 boron atoms) + 63.55 g/mol (7 oxygen atoms)
Molar mass = 381.37 g/mol
Moles = mass / molar mass
Moles = 6780 g / 381.37 g/mol
Moles = 17.782 moles
Now we can calculate the molarity using the formula:
Molarity (M) = 17.782 moles / 45.0 L
Molarity = 0.395 M
c. To find the number of moles of sodium borate in 600.0 mL of a 1.57 M solution:
First, we need to convert milliliters to liters:
600.0 mL = 0.6 L
Then we can use the molarity formula:
Moles = Molarity × volume
Moles = 1.57 M × 0.6 L
Moles = 0.942 moles
So, there are 0.942 moles of sodium borate in 600.0 mL of a 1.57 M solution.
d. To find the volume of a 1.87 M solution that contains 50.8 g of sodium borate:
First, we need to convert grams to moles by dividing by the molar mass of sodium borate:
Molar mass = 381.37 g/mol
Moles = mass / molar mass
Moles = 50.8 g / 381.37 g/mol
Moles = 0.133 moles
Now we can calculate the volume using the molarity formula:
Volume = moles / Molarity
Volume = 0.133 moles / 1.87 M
Volume = 0.071 L
Finally, we need to convert the volume from liters to milliliters:
0.071 L = 71 mL
So, 71 mL of a 1.87 M solution contains 50.8 g of sodium borate.
a. To find the molarity of a solution, you need to divide the number of moles of solute by the volume of the solution in liters.
So in this case, the number of moles of sodium borate is given as 1.85 moles, and the volume of the solution is given as 2.50 L.
Molarity (M) = Number of moles of solute / Volume of solution in liters
M = 1.85 moles / 2.50 L = 0.74 M
Therefore, the molarity of the solution is 0.74 M.
b. Similar to part (a), you need to divide the number of moles of sodium borate by the volume of the solution in liters.
The number of moles of sodium borate is given as 6.78 kg. First, we need to convert this mass from kilograms to grams by multiplying by 1000 because molar mass is usually given in grams.
6.78 kg * 1000 g/kg = 6780 g
Next, we need to calculate the number of moles of sodium borate. To do this, divide the mass of sodium borate by its molar mass. The molar mass of sodium borate (Na2B4O7) is the sum of the atomic masses of the elements in its formula:
2(23) + 4(10.8) + 7(16) = 22 + 43.2 + 112 = 177.2 g/mol
Number of moles = Mass / Molar mass
Number of moles = 6780 g / 177.2 g/mol = 38.28 moles
Finally, divide the number of moles by the volume of the solution in liters to find the molarity:
Molarity = Number of moles / Volume of solution in liters
Molarity = 38.28 moles / 45.0 L = 0.851 M
Therefore, the molarity of the solution is 0.851 M.
c. Given that the volume of the solution is 600.0 mL (which is equivalent to 0.600 L) and the molarity of the sodium borate solution is 1.57 M, we can use the formula for molarity to find the number of moles of sodium borate.
Molarity = Number of moles / Volume of solution in liters
Rearranging the formula, we get:
Number of moles = Molarity * Volume of solution in liters
Number of moles = 1.57 M * 0.600 L = 0.942 moles
Therefore, there are 0.942 moles of sodium borate in 600.0 mL of a 1.57 M sodium borate solution.
d. To find the volume of the solution needed to contain 50.8 g of sodium borate, we can use the formula for molarity:
Molarity = Number of moles / Volume of solution in liters
Rearranging the formula, we get:
Volume of solution in liters = Number of moles / Molarity
First, we need to calculate the number of moles of sodium borate. To do this, divide the mass of sodium borate by its molar mass. Again, the molar mass of sodium borate is 177.2 g/mol.
Number of moles = Mass / Molar mass
Number of moles = 50.8 g / 177.2 g/mol = 0.287 moles
Now we can calculate the volume of the solution in liters:
Volume of solution in liters = 0.287 moles / 1.87 M = 0.153 L
To convert liters to milliliters, multiply by 1000:
Volume of solution in mL = 0.153 L * 1000 mL/L = 153 mL
Therefore, 153 mL of a 1.87 M solution contains 50.8 g of sodium borate.