A 500-mL sample of effluent from a chemical plant contains 26.1 μg of mercury. If the density of the effluent liquid is 1.073 g/mL, calculate the concentration of mercury in (a) molarity and (b) parts per million.

Sure, let's solve this step by step.

(a) Molarity

First, we need to convert the mass of mercury from micrograms (μg) to grams (g) because the molar mass of mercury (Hg) is usually given in g/mol.

1 μg = 1e-6 g

So, 26.1 μg = 26.1 * 1e-6 g = 2.61e-5 g

The molar mass of mercury (Hg) is 200.59 g/mol.

So, the number of moles of mercury = mass/molar mass = 2.61e-5 g / 200.59 g/mol = 1.3e-7 mol

The volume of the solution is given in mL, we need to convert it to liters (L) because molarity is defined as moles/Liter.

500 mL = 0.5 L

So, the molarity (M) = moles/volume = 1.3e-7 mol / 0.5 L = 2.6e-7 M

(b) Parts per million (ppm)

ppm is defined as the mass of the solute divided by the mass of the solution, multiplied by 1,000,000.

First, we need to find the mass of the solution.

The density of the solution is given as 1.073 g/mL, so the mass = density * volume = 1.073 g/mL * 500 mL = 536.5 g

So, the concentration of mercury in ppm = (mass of Hg / mass of solution) * 1,000,000 = (2.61e-5 g / 536.5 g) * 1,000,000 = 0.049 ppm.

To solve this problem, we need to follow these steps:

Step 1: Convert the volume of the effluent from mL to L: 500 mL = 0.5 L

Step 2: Convert the mass of mercury from μg to g: 26.1 μg = 0.0000261 g

Step 3: Convert the mass of mercury from g to moles. The atomic mass of mercury (Hg) is approximately 200.59 g/mol, so: 0.0000261 g ÷ 200.59 g/mol = 1.3 x 10^-7 mol

Step 4: Calculate the molarity (M) of mercury in the effluent. Molarity is defined as the number of moles of solute per liter of solution, so: 1.3 x 10^-7 mol ÷ 0.5 L = 2.6 x 10^-7 M

This is the answer to part (a).

Step 5: Calculate the concentration of mercury in parts per million (ppm). ppm is defined as the mass of the solute divided by the mass of the solution, multiplied by 1,000,000. First, we need to find the mass of the solution. We know the volume of the solution and its density, so we can find the mass by multiplying these two values: 0.5 L x 1.073 g/mL x 1000 mL/L = 536.5 g

Then, we can find the concentration in ppm: 0.0000261 g ÷ 536.5 g x 1,000,000 = 0.0487 ppm

This is the answer to part (b).