Question

The "alum" used in cooking is potassium aluminum sulfate hydrate, $KAl(S{O}_3{)}_2\cdot x{H}_{2}O$. To find the value of x, a sample of the compound is heated. The mass of the empty crucible is $20.01g$.
The alum hydrate was added to the crucible until the total mass of the crucible and hydrate was $24.75g$. The sample was heated in the crucible until the final mass of the crucible and anhydrous product was $22.5g$.
What is the value of x?

• A. $2$
• B. $3$
• C. $12$
• D. $18$

Answer 1

Answer: (C)

$12$

Mass of crucible Hydrate $=24.75$

Mass of hydrate $=24.75-20.01=4.74$ $g$

Mass of anhydrate $=22.5-20.01=2.49$ $g$

$KAl(S{O}_3{)}_2\cdot x{H}_{2}O⟶KAl(S{O}_3{)}_2+x{H}_{2}O$

Mass: $(18x+226)$ $g$ Mass $=226$ $g$

$(226+18x)$ $g$ $\stackrel{gives}{⟶}$ $226$ $g$

$4.74$ $g$ $\stackrel{gives}{⟶}$ $2.49$ $g$

$\frac{226+18x}{4.74g}=\frac{226}{2.49}$

$x\approx 12$