Atkins - Abundância percentual

por Alberto Nascente Qua 23 Nov 2022, 17:36

A massa molar dos átomos de boro de uma amostra natural é 10,81 g.mol^-1
Sabe-se que a amostra contém ¹⁰B (massa molar 10,013 g.mol^-1) e ¹¹B (massa molar 10,093 g.mol^-1)
Quais são as abundâncias percentuais dos dois isótopos?

Fiz da seguinte maneira:

Atkins - Abundância percentual Svg+xml;base64,<?xml version='1.0' encoding='UTF-8'?>
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, em que x + y = 1

Nisso, fiz uma substituição e encontrei que:

Está certinho?
Obrigado! Very Happy

por André Meneses Qua 23 Nov 2022, 22:51

Se você substituir os valores que você achou na equação, vai ver que x*10,013 + y*10,093 = 10,02097, valor diferente de 10,81. Lembrando que x + y = 1 e x,y > 0. Logo, dada uma abundância x de um isótopo, a abundância do outro será 1-x. Se você substituir y por 1-x vai achar os valores corretos.

por Alberto Nascente Qui 24 Nov 2022, 08:31

Ue, mas pq eu não poderia usar o 10,81 ?
E de onde saiu esse valor 10,02097?

Se eu substituir oq o senhor disse na equação x*10,013 + y*10,093 = 10,02097 eu acho que:
x = 0,900375
y = 0,099625

Mas não entendi, pq eu achei os mesmos valores q achei na conta da 1ª mensagem...

Obrigado!

por André Meneses Qui 24 Nov 2022, 16:24

Você deve usar o 10,81. O problema é que com os valores de x e y que você achou, o resultado não é 10,81.

0,900375*10,013 + 10,093*0,099625 = 10,02097, que é diferente de 10,81. Portanto os valores de x e y que você achou estão errados.

Mas da maneira que você colocou, a questão tem um problema. Não tem como uma combinação de massas de 10,013 e 10,093 dar 10,81. Certeza que não é 10,081?

por Alberto Nascente Qui 24 Nov 2022, 19:07

Tenho certeza, copiei igualzinho ao enunciado do livro físico.
Deve ser um erro de digitação mesmo...
Mas enfim, consegui entender a essência da questão, mesmo com o erro.

Obrigado! Very Happy