What volume of ethanol must be diluted with

water to prepare 674 mL of 0.854 M solution?
The density of ethanol is given as 0.789 g/mL.
Answer in units of mL

You need a total volume of 674mL=0.674L

Solve for moles of ethanol:

Moles=Molarity*Volume (L)

Moles=0.854 M*0.674L

Moles of ethanol*(46.07g/mole)= mass of ethanol

Density=Mass/Volume

So,

Mass/Density=Volume (mL)

Mass of ethanol/0.789 g/mL=Volume (mL)

To find the volume of ethanol needed, we need to first calculate the mass of ethanol required, and then use the density of ethanol to convert it to volume.

Step 1: Calculate the moles of ethanol required.

Molarity (M) is defined as moles of solute per liter of solution. Therefore, to find the moles of ethanol required, we can use the formula:

moles of ethanol = Molarity x volume of solution (in liters)

Given:
Molarity (M) = 0.854 M
Volume of solution = 674 mL = 0.674 L

moles of ethanol = 0.854 M x 0.674 L

Step 2: Calculate the mass of ethanol required.

The molar mass of ethanol is 46.07 g/mol.

mass of ethanol = moles of ethanol x molar mass of ethanol

mass of ethanol = (0.854 M x 0.674 L) x 46.07 g/mol

Step 3: Convert the mass of ethanol to volume.

Given:
Density of ethanol = 0.789 g/mL

volume of ethanol = mass of ethanol / density of ethanol

volume of ethanol = (0.854 M x 0.674 L x 46.07 g/mol) / 0.789 g/mL

The volume of ethanol that must be diluted with water to prepare 674 mL of 0.854 M solution is approximately 531.74 mL.

To determine the volume of ethanol that must be diluted, we first need to calculate the amount of ethanol required to make a 0.854 M solution.

The formula for calculating the amount of solute required is:

Amount of solute (in moles) = Molarity (in M) × Volume of solution (in liters)

Since we want the answer in milliliters, we need to convert the volume of solution to liters. Therefore, we have:

Volume of solution = 674 mL = 674/1000 L = 0.674 L
Molarity = 0.854 M

Now, we can calculate the moles of ethanol required:

Amount of ethanol (in moles) = 0.854 M × 0.674 L

Next, we need to calculate the mass of ethanol required:

Mass of ethanol (in grams) = Amount of ethanol (in moles) × Molar mass of ethanol

The molar mass of ethanol (C2H5OH) can be calculated using the atomic masses of carbon (C), hydrogen (H), and oxygen (O). Adding them together, we get:

Molar mass of ethanol = 2 × Atomic mass of carbon + 6 × Atomic mass of hydrogen + 1 × Atomic mass of oxygen

= 2 × 12.01 g/mol + 6 × 1.01 g/mol + 1 × 16.00 g/mol
= 24.02 g/mol + 6.06 g/mol + 16.00 g/mol
= 46.08 g/mol

Now, we can calculate the mass of ethanol required:

Mass of ethanol (in grams) = Amount of ethanol (in moles) × Molar mass of ethanol
= (0.854 M × 0.674 L) × 46.08 g/mol

Finally, we can convert the mass of ethanol to volume using the density of ethanol. The formula for calculating volume using density is:

Volume (in mL) = Mass (in g) / Density (in g/mL)

Thus, the volume of ethanol required is:

Volume of ethanol = (Mass of ethanol (in grams) / Density of ethanol)
= [(0.854 M × 0.674 L) × 46.08 g/mol] / 0.789 g/mL

By plugging in the values and performing the calculations, you will be able to find the volume of ethanol required to prepare a 674 mL of 0.854 M solution.