Question

determination of a chemical formula data
atomic mass: copper 63.546 cl 35.453 h 1.008 o 15.999
mass of crucible 33.637 g
mass of crucible & hydrated sample 34.287 g
mass of hydrated sample 0.650 g
mass of crucible & dehydrated sample 34.141 g
mass of dehydrated sample 0.504 g
mass of filter paper 0.283 g
mass of copper 0.623 g on filter paper
no. moles of copper ____ moles
mass of water evolved 0.146 g
no. moles of water ____ moles
mass of chlorine in sample ____ g
no. mole of chlorine ____ moles
mole ratio, chlorine : coper in sample ____ : 1
mole ratio, water : copper in hydrated sample ____ : 1
formula of dehydrated sample ____
formula of hydrated sample ____

Explanation:

Step1: Calculate moles of copper

Use the formula $n=\frac{m}{M}$, where $n$ is moles, $m$ is mass and $M$ is molar - mass. Given mass of copper $m = 0.623g$ and molar - mass of copper $M=63.546g/mol$.
$n_{Cu}=\frac{0.623g}{63.546g/mol}\approx0.0098mol$

Step2: Calculate moles of water

Given mass of water evolved $m = 0.146g$ and molar - mass of water $M = 18.015g/mol$. Using $n=\frac{m}{M}$, we get $n_{H_2O}=\frac{0.146g}{18.015g/mol}\approx0.0081mol$

Step3: Calculate mass of chlorine in sample

Mass of hydrated sample is $0.650g$, mass of copper is $0.623g$ and mass of water evolved is $0.146g$. Mass of chlorine $m_{Cl}=0.650g - 0.623g-0.146g$ (this is incorrect way, we should use other data). Mass of dehydrated sample is $0.504g$, mass of copper is $0.623g$ (subtracting filter paper mass etc.). Mass of chlorine in sample: Mass of dehydrated sample - Mass of copper in sample. But we assume the correct way is to use the fact that in a compound, we can find mass of chlorine from the difference in masses of the sample components. Let's assume the sample contains only copper, chlorine and water in hydrated form. Mass of chlorine $m_{Cl}=0.504g - 0.623g+ 0.283g=0.164g$

Step4: Calculate moles of chlorine

Using $n=\frac{m}{M}$, with $m = 0.164g$ and $M = 35.453g/mol$, $n_{Cl}=\frac{0.164g}{35.453g/mol}\approx0.0046mol$

Step5: Calculate mole ratio of chlorine to copper

$r_{Cl:Cu}=\frac{n_{Cl}}{n_{Cu}}=\frac{0.0046mol}{0.0098mol}\approx0.47:1\approx1:2$

Step6: Calculate mole ratio of water to copper

$r_{H_2O:Cu}=\frac{n_{H_2O}}{n_{Cu}}=\frac{0.0081mol}{0.0098mol}\approx0.83:1\approx1:1.2$ (rounding to nearest whole - number ratio)

Step7: Determine formula of dehydrated sample

Since the mole ratio of $Cl:Cu\approx1:2$, the formula of the dehydrated sample is $CuCl_2$

Step8: Determine formula of hydrated sample

Based on the mole ratio of $H_2O:Cu\approx1:1$, the formula of the hydrated sample is $CuCl_2\cdot H_2O$

Answer:

Moles of copper: $0.0098$ moles
Moles of water: $0.0081$ moles
Mass of chlorine in sample: $0.164g$
Moles of chlorine: $0.0046$ moles
Mole ratio, Chlorine : Copper in sample: $1:2$
Mole ratio, water : Copper in hydrated sample: $1:1$
Formula of dehydrated sample: $CuCl_2$
Formula of hydrated sample: $CuCl_2\cdot H_2O$