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Chapter 21: Problem 90

How many different pentapeptides can be formed using five different amino acids?

Short Answer

Expert verified
There are 120 different pentapeptides that can be formed using the given five amino acids. This is calculated using the permutation formula \(P(n, r) = \frac{n!}{(n-r)!}\), where n is the number of amino acids and r is the number of positions to fill. In this case, \(P(5, 5) = \frac{5!}{(5-5)!} = \frac{120}{1} = 120\).

Step by step solution

01

Define the problem

We need to find the number of ways to arrange five different amino acids to form pentapeptides. Since a pentapeptide has five positions for the amino acids, we will be arranging the five amino acids to fill these positions without repetition.
02

Permutation formula

The permutation formula, denoted by P(n, r), is a way to find the number of ways to arrange 'n' items in 'r' positions without repetition. The formula is: P(n, r) = n!/(n-r)! In our case, we have 5 different amino acids and 5 positions to fill, so n=5 and r=5.
03

Calculate the factorial of n and n-r

First, we need to calculate the factorial of 'n' (5) and 'n-r' (0): - 5! = 5 × 4 × 3 × 2 × 1 = 120. - 0! is defined as 1.
04

Calculate the permutations using the formula

Now, we can calculate P(5, 5) using the formula. P(5, 5) = 120/1 = 120
05

Write the final answer

There are 120 different pentapeptides that can be formed using the given five amino acids.

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Most popular questions from this chapter

In glycine, the carboxylic acid group has \(K_{\mathrm{a}}=4.3 \times 10^{-3}\) and the amino group has \(K_{b}=6.0 \times 10^{-5} .\) Use these equilibrium constant values to calculate the cquilibrium constants for the following. a. \(^{+} \mathrm{H}_{3} \mathrm{NCH}_{2} \mathrm{CO}_{2}^{-}+\mathrm{H}_{2} \mathrm{O} \rightleftharpoons \mathrm{H}_{2} \mathrm{NCH}_{2} \mathrm{CO}_{2}^{-}+\mathrm{H}_{3} \mathrm{O}^{+}\) b. \(\mathrm{H}_{2} \mathrm{NCH}_{2} \mathrm{CO}_{2}^{-}+\mathrm{H}_{2} \mathrm{O} \rightleftharpoons \mathrm{H}_{2} \mathrm{NCH}_{2} \mathrm{CO}_{2} \mathrm{H}+\mathrm{OH}^{-}\) c. \(\mathbf{H}_{3} \mathrm{NCH}_{2} \mathrm{CO}_{2} \mathrm{H} \rightleftharpoons 2 \mathrm{H}^{+}+\mathrm{H}_{2} \mathrm{NCH}_{2} \mathrm{CO}_{2}^{-}\)

The Amoco Chemical Company has successfully raced a car with a plastic engine. Many of the engine parts, including piston skirts, connecting rods, and valve- train components, were made of a polymer called Torlon: What monomers are used to make this polymer?

Draw a structural formula for each of the following. a. 3 -methylpentanoic acid b. ethyl methanoate c. methyl benzoate d. 3 -chloro- 2,4 -dimethylhexanoic acid

Draw the structural formula for each of the following. a. 3 -isobutylhexane b. 2,2,4 -trimethylpentane, also called isooctane. This substance is the reference (100 level) for octane ratings. c. 2 -tert-butylpentane d. The names given in parts a and c are incorrect. Give the correct names for these hydrocarbons.

A polypeptide is also called a polyamide. Nylon is also an example of a polyamide. What is a polyamide? Consider a polyhydrocarbon, a polyester, and a polyamide. Assuming average chain lengths are equal, which polymer would you expect to make the strongest fibers and which polymer would you expect to make the weakest fibers? Explain.
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