The density of acetonitrile, CH3CN, is 0.786 g/mL, and the density of methanol, CH3OH,

is 0.791 g/mL. A solution is made by dissolving 15.0 g of methanol in 250.0 mL of
acetonitrile. Assuming that the volumes of the solute and solvent are additive, what is the
molarity of methanol in the solution?

M methanol = mols methanol/L solution.

mols methanol = grams/molar mass = ?
L solution = volume methanol + acetonitrile.

Convert g methanol to mL methanol using density. Add to volume of acetonitile (mL + mL) and convert to L. Plug L into the mols/L above and solve for M methanol.

To find the molarity of methanol in the solution, we need to first calculate the number of moles of methanol and then divide it by the volume of the solution in liters.

Step 1: Calculate the number of moles of methanol.
The molar mass of methanol (CH3OH) is:
C = 12.01 g/mol
H = 1.01 g/mol (3 hydrogen atoms)
O = 16.00 g/mol
Total molar mass = 32.04 g/mol

To find the number of moles of methanol, we use the formula:
moles = mass / molar mass

mass of methanol = 15.0 g
moles of methanol = 15.0 g / 32.04 g/mol

Step 2: Calculate the volume of the solution in liters.
The volume of the solution is given as 250.0 mL. We need to convert it to liters.
1 mL = 0.001 L

volume of solution = 250.0 mL × 0.001 L/mL

Step 3: Calculate the molarity of methanol.
Molarity is defined as the moles of solute divided by the volume of the solution in liters.
Molarity (M) = moles of methanol / volume of solution (in liters)

Using the values calculated in Step 1 and Step 2, we can calculate the molarity of methanol:

Molarity = (15.0 g / 32.04 g/mol) / (250.0 mL × 0.001 L/mL)

Now you can substitute the values and calculate the molarity.

To find the molarity of methanol in the solution, we first need to calculate the number of moles of methanol dissolved in the acetonitrile solution.

Step 1: Calculate the volume of methanol in liters.
Given that the density of methanol is 0.791 g/mL and we have 15.0 g of methanol, we can use the density to convert the mass to volume:

Volume of methanol = (15.0 g) / (0.791 g/mL) = 18.97 mL

However, we need to convert this volume to liters to maintain consistency with the units we'll be using for molarity. Since 1 L = 1000 mL:

Volume of methanol in liters = 18.97 mL / 1000 = 0.01897 L

Step 2: Calculate the number of moles of methanol.
To calculate the number of moles, we can use the formula:

moles = mass / molar mass

The molar mass of methanol (CH3OH) can be calculated by summing the individual atomic masses:

C = 12.01 g/mol
H = 1.01 g/mol (3 hydrogen atoms)
O = 16.00 g/mol

Molar mass of methanol (CH3OH) = (12.01 g/mol) + (1.01 g/mol x 4) + 16.00 g/mol = 32.04 g/mol

moles of methanol = (15.0 g) / (32.04 g/mol) = 0.468 moles

Step 3: Calculate the volume of acetonitrile in liters.
Given that the density of acetonitrile is 0.786 g/mL and we have 250.0 mL of acetonitrile, convert the volume to liters:

Volume of acetonitrile = (250.0 mL) / (1000 mL/L) = 0.250 L

Step 4: Calculate the molarity of methanol.
Molarity (M) is defined as moles of solute per liter of solution. In this case, the solute is methanol and the solvent is acetonitrile.

Molarity of methanol = moles of methanol / volume of acetonitrile in liters

Molarity of methanol = (0.468 moles) / (0.250 L) = 1.872 M

Therefore, the molarity of methanol in the solution is 1.872 M.