Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 22: 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 five different amino acids. This is calculated using the permutation formula \(P(5,5) = \frac{5!}{(5-5)!} = 120\).

Step by step solution

01

Identify number of different amino acids available

We have 5 different amino acids to arrange in a pentapeptide.
02

Understand permutations

Permutation is the arrangement of objects in a specific order. In this case, we want to find all possible arrangements of the 5 different amino acids. A formula for calculating permutations is given by: \[P(n,r) = \frac{n!}{(n-r)!}\] Where n is the total number of elements and r is the number of elements to be arranged. In this problem, we have 5 different amino acids and we need to arrange all the 5, so n = 5 and r = 5.
03

Apply the permutation formula

Now, let's apply the permutation formula to calculate the total number of unique arrangements that can be formed using the 5 different amino acids: \[P(5,5) = \frac{5!}{(5-5)!}\]
04

Solve for pentapeptides

We can now proceed to calculate the factorial values of 5! and 0!: \[5! = 5 \times 4 \times 3 \times 2 \times 1 = 120\] \[0! = 1\] Now, plug these factorial values back into the permutation formula: \[P(5,5) = \frac{120}{1} = 120\] Hence, there are 120 different pentapeptides that can be formed using five different amino acids.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Kevlar, used in bulletproof vests, is made by the condensation copolymerization of the monomers Nc1ccc(N)cc1 and O=C(O)c1ccc(C(=O)O)cc1 Draw the structure of a portion of the Kevlar chain.

Draw all the structural and geometrical (cis-trans) isomers of bromochloropropene.

A chemical "breathalyzer" test works because ethanol in the breath is oxidized by the dichromate ion (orange) to form acetic acid and chromium(III) ion (green). The balanced reaction is \(3 \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(a q)+2 \mathrm{Cr}_{2} \mathrm{O}_{7}{ }^{2-}(a q)+2 \mathrm{H}^{+}(a q) \longrightarrow\) \(3 \mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}(a q)+4 \mathrm{Cr}^{3+}(a q)+11 \mathrm{H}_{2} \mathrm{O}(l)\) You analyze a breathalyzer test in which \(4.2 \mathrm{mg} \mathrm{K}_{2} \mathrm{Cr}_{2} \mathrm{O}_{7}\) was reduced. Assuming the volume of the breath was \(0.500 \mathrm{~L}\) at \(30 .{ }^{\circ} \mathrm{C}\) and \(750 . \mathrm{mm} \mathrm{Hg}\), what was the mole percent alcohol of the breath?

Name all the alcohols that have the formula \(\mathrm{C}_{5} \mathrm{H}_{12} \mathrm{O}\). How many ethers have the formula \(\mathrm{C}_{5} \mathrm{H}_{12} \mathrm{O}\) ?

Aspartame, the artificial sweetener marketed under the name Nutra-Sweet, is a methyl ester of a dipeptide: a. What two amino acids are used to prepare aspartame? b. There is concern that methanol may be produced by the decomposition of aspartame. From what portion of the molecule can methanol be produced? Write an equation for this reaction.
See all solutions

Recommended explanations on Chemistry Textbooks

Chemical Analysis

Read Explanation

Inorganic Chemistry

Read Explanation

The Earths Atmosphere

Read Explanation

Chemistry Branches

Read Explanation

Making Measurements

Read Explanation

Organic Chemistry

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free