Answer :
Answer:-
3.77 x 10²¹ arsenic(iii) oxide molecules correspond to an LD50 value of 0.0146 for a 187 lb man
Explanation: -
Weight of man = 187 lb
= [tex]\frac{187 lb}{2.2 lb} x 1 kg[/tex]
= 84.8 Kg
LD50 = number of grams of a substance that is lethal to 50% of animals per kilogram of body weight
0.0146 = [tex]\frac{number of grams }{Weight of man in kg}[/tex]
Thus
Number of grams of lethal substance = 0.0146 x 84.8
= 1.24 g
Molar mass of arsenic(iii) oxide = 197.841 g/mol
Number of moles of arsenic(iii) oxide = [tex]\frac{Mass}{Molar mass}[/tex]
= [tex]\frac{1.24}{197.841}[/tex]
= 0.00627 moles
Number of molecules of arsenic(iii) oxide = Number of moles x Avogadro number
= 0.00627 x 6.02 x 10²³
= 3.77 x 10²¹
Final answer:
To calculate the number of arsenic(III) oxide molecules corresponding to an LD50 value for a 187-pound man, convert the man's weight to kilograms, find the lethal dose in grams, convert this to moles using the molar mass of As₂O₃, and then calculate the number of molecules using Avogadro's number, resulting in approximately 3.767 × 1021 molecules.
Explanation:
To calculate the number of arsenic(III) oxide molecules corresponding to an LD50 value of 0.0146 for a 187-pound man, assuming that the test animals and humans have the same LD50, follow these steps:
Convert the man's weight from pounds to kilograms. 1 pound is approximately 0.453592 kilograms. Hence, 187 pounds is approximately 84.821 kilograms.
Multiply the LD50 value by the man's weight in kilograms to find the lethal dose in grams: 0.0146 g/kg × 84.821 kg = 1.2384 grams.
To find the number of molecules, convert the mass of arsenic(III) oxide to moles using its molecular weight (As₂O₃ has a molar mass of approximately 197.84 g/mol), and then multiply by Avogadro's number (6.022 × 1023 molecules/mol).
1.2384 g ÷ 197.84 g/mol = 0.006258 mol × 6.022 × 1023 molecules/mol = 3.767 × 1021 molecules of arsenic(III) oxide.
This calculation shows the number of molecules of arsenic(III) oxide corresponding to the LD50 for a 187-pound man.
