How would you tell the difference between chiral and achiral structures?

For example:
1. #H_3C CHBrCH_2CH_3#
2.#PCl_2BrCH_3^+#
3.#Cl_3C CHFBr#
4.#HC# triple bonded to #C CF_3#
5.#CH_2Cl_3#
6.#HPClBrCH_3^+#
7.#F_3C CBr_3#
8.#H_3CBr#?

Answer 1

Well, the best advice is to simply make a model of the mirror images of each compound....but given such a string of compounds this is not really practical...

Now for a chiral molecule we look for a carbon that has four DIFFERENT substituents...#CR_1R_2R_3R_4#...which can potentially generate LEFT-HANDED and RIGHT-HANDED stereoisomers about carbon....

The isomer on OUR LEFT (as we face the page) is appropriately the #"S-stereoisomer"#, and the isomer on the RIGHT is the #"R-stereoisomer"#. And given this geometry the INTERCHANGE of ANY TWO substituents at the chiral carbon will give rise to the enantiomer...and interchange again, you get the enantiomer of an enantiomer, i.e. the original stereoisomer.

And so we look at the structures of the given molecules to try to identify any potential chiral centres..with a star

#1.# #H_3C-stackrel"*"CHBrCH_2CH_3#

#2.# #{PCl_2BrCH_3}^+#...the phosphorus is ACHIRAL

#3.# #Cl_3C-stackrel"*"CHFBr#

#4.# #HC-=C-CF_3# ….no chiral centres...

#5.# #CH_2Cl_3#...this is not a cromulent organic molecule... (I just wanted to use that word because Homer Simpson uses it.)

#6.# #{HP(Cl)(Br)(CH_3)}^+#...the phosphorus in this phosphonium ion is potentially chiral....but this would be a hard beast to isolate...

#7.# #F_3C-CBr_3#....no chiral centres...

#8.# #H_3CBr#...#"methyl bromide"# is ACHIRAL...

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Answer 2

Chiral structures lack a plane of symmetry, meaning they cannot be superimposed on their mirror image. Achiral structures possess a plane of symmetry and can be superimposed on their mirror image.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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