Calculate the molar concentration for each of the following.
a)The concentration of a brine solution containing 225 g for pure sodium chloride dissolved in 4.00 L of solution.
b)The volume that must be added to 4.2 mol of magnesium chloride to make a 0.045 M solution.
c)The concentration of ethanol that is considered the legal limit when driving: 0.08 g of C2H6O(1) in 100 mL of blood.
For all of these just follow the definition that M = mols/L solution.
a. mols NaCl = grams NaCl/molar mass NaCl
Then M = mols L = ?
b. M = mols/L. You know mols and M, solve for L.
c. Convert 0.08g to mols. mols = grams/molar mass = ?
That many mols in 0.1 L means ? mols ethanol in 1 L? That gives you M.
a) To calculate the molar concentration, we first need to find the number of moles of solute (sodium chloride) and then divide it by the volume of the solution.
1. Start by finding the molar mass of sodium chloride (NaCl). The atomic mass of sodium (Na) is approximately 23 g/mol, and the atomic mass of chlorine (Cl) is approximately 35.5 g/mol. So the molar mass of NaCl is 23 + 35.5 = 58.5 g/mol.
2. Next, calculate the number of moles of sodium chloride by dividing the given mass (225 g) by its molar mass (58.5 g/mol). This gives us:
Number of moles = 225 g / 58.5 g/mol
3. Now, we need to divide the number of moles by the volume of the solution (4.00 L) to get the molar concentration:
Molar concentration (mol/L) = Number of moles / Volume
b) In this case, we are given the number of moles and asked to find the volume of the solution.
1. Start by using the equation for molar concentration:
Molar concentration (mol/L) = Number of moles / Volume
2. Rearrange the equation to solve for Volume:
Volume = Number of moles / Molar concentration
Plug in the given values:
Number of moles = 4.2 mol
Molar concentration = 0.045 M
Substitute these values into the equation to find the volume in liters.
c) For this question, we are given the mass of ethanol and the volume of blood, and we need to calculate the concentration:
1. The molecular formula for ethanol is C2H6O. To find its molar mass, add up the atomic masses of carbon (C), hydrogen (H), and oxygen (O). The atomic masses are approximately 12 g/mol, 1 g/mol, and 16 g/mol, respectively. So the molar mass of C2H6O is:
2 * 12 g/mol + 6 * 1 g/mol + 1 * 16 g/mol = 46 g/mol
2. Calculate the number of moles of ethanol by dividing the given mass (0.08 g) by its molar mass (46 g/mol):
Number of moles = 0.08 g / 46 g/mol
3. Finally, divide the number of moles by the volume of blood (100 mL = 0.1 L) to get the molar concentration:
Molar concentration (mol/L) = Number of moles / Volume
Note that in this case, the initial volume is given in milliliters, so it should be converted to liters by dividing by 1000.