Chemical equation

Chemistry Level 1

$a\text{Al}_2 \text O_3 + b\text{HCl} = c\text{AlCl}_3 + d\text H_2 \text O.$

Find the minimum value of $a + b + c +d,$ where $a,b,c,d \in \mathbb{N}.$

1 solution

X X
Aug 7, 2018

$\text{Al}_2 \text O_3 + 6\text{HCl} \to 2\text{AlCl}_3 + 3\text H_2 \text O.$ (I think it should be an arrow instead of "=")

Notice $\text{Al}$ ,we get $c=2a$

Notice $\text{O}$ ,we get $d=3a$

Notice $\text{H}$ ,we get $b=2d$

Notice $\text{Cl}$ ,we get $b=3c$

So, $a:b:c:d=1:6:2:3$