Question

A 70−kg ⁷⁰ −kg adult can die from injection of −100ng∼100ng of botulinum neurotoxin or by inhaling −1μg∼1μg of the toxin. A sensitive assay for the neurotoxin can detect −200pg/mL∼200pg/muL in 60μL60μL of milk or juice.

a. How many moles of neurotoxin (molecular mass 150000 g/mol)150000 g/mol ) are in 60μL60μL containing 200pgmL2200pg/mL ? Express your answer with a prefix from Table 1.3.
b. How many molecules are in 100ng100ng of neurotoxin?

Answer 1

To find the amount of neurotoxin in moles in a 60μl solution, multiply concentration by volume and divide by molecular mass. For the number of molecules in 100 ng, convert mass to moles, then use Avogadro's number to convert moles to molecules.

Step-by-step explanation:

To answer part a, we need to determine how many moles of botulinum neurotoxin are in 60μl of solution with a concentration of 200 pg/mL. First, we will convert 200 pg/mL to grams per liter (1 pg = 1 x 10-12 g):
200 pg/mL x 1 g / 1 x 1012 pg = 2 x 10-10 g/mL
Next, convert to grams per liter (1000 mL = 1 L):
2 x 10-10 g/mL x 1000 mL/L = 2 x 10-7 g/L
Now, we find the total grams in 60 μl:
60 μl = 60 x 10-6 L
2 x 10-7 g/L x 60 x 10-6 L = 1.2 x 10-11 g
Finally, to determine the number of moles, divide by the molecular mass:
1.2 x 10-11 g ÷ 150,000 g/mol = 8 x 10-17 moles.

For part b, to calculate the number of molecules in 100 ng of neurotoxin, we take into account that
100 ng = 1 x 10-10 g, and using Avogadro's number (6.022 x 1023 molecules/mol):
Number of moles = 1 x 10-10 g ÷ 150,000 g/mol = 6.67 x 10-16 mol
Number of molecules = 6.67 x 10-16 mol x 6.022 x 1023 molecules/mol = 4.01 x 108 molecules.