Iodometric analysis of high-temperature superconductor. The procedure in Box16 - 3 was carried out to find the effective copper oxidation state, and therefore the number of oxygen atoms, in the formula ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_7$, where $0\le \mathrm{z}\le 0.5$.

(a) In Experiment A of Box 16 - 3, 1.00 g of superconductor required 4.55 mmol of role="math" localid="1654948290716" ${\mathrm{S}}_2{\mathrm{O}}_3^{2-}$. In Experiment B,1.00 g of superconductor required 5.68 mmol of${\mathrm{S}}_2{\mathrm{O}}_3^{2-}$ Calculate the value of z in the formula ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-\mathrm{z}}$(FM ).

(b) Propagation of uncertainty. In several replications of Experiment A, the thiosulfate required was $4.55(\pm 0.010)$mmol of role="math" localid="1654948278531" ${\mathrm{S}}_2{\mathrm{O}}_3^{2-}$ per gram of ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_7$. In ExperimentB, the thiosulfate required was $5.68(\pm 0.05)\mathrm{mmol}$ of ${\mathrm{S}}_2{\mathrm{O}}_3^{2-}$per gram. Calculate the uncertainty x of in the formula${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{\mathrm{x}}$.

• The mole concept is a simple way to express the amount of a substance. Any measurement is divided into two parts: the numerical magnitude and the units in which the magnitude is expressed. For example, if the mass of a ball is 2 kilogrammes, the magnitude is '2' and the unit is 'kilogramme.'
• When dealing with particles at the atomic (or molecular) level, even one gramme of a pure element is known to contain a large number of atoms. This is a common application of the mole concept. It primarily focuses on the unit known as a'mole,' which is a count of a very large number of particles.

a) In this task, we need to determine the number of O atoms in the given formula.

When ${\mathrm{YBaBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_7$is heated, it loses an oxygen atom and the molecular formula for the compound is between ${\mathrm{YBaBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_7$and localid="1654948856793" ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_6$.

We have formula ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-z}$where the z is from 0 to 0.5 .

Therefore, ${\mathrm{YBaBCu}}_3{\mathrm{O}}_7$contains one ${\mathrm{Cu}}^{3+}$and two ${\mathrm{Cu}}^{2+}$, while ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6.5}$contains only three ${\mathrm{Cu}}^{2+}$So, the moles of ${\mathrm{Cu}}^{3+}$in the ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-z}$is 1-2z

The moles of the superconductor can be calculated using the mass (1g) and molar mass(666.24615.9994g/mol ):

The difference in ${\mathrm{S}}_2{\mathrm{O}}_3^{2-}$required between experiments B and A gives the ${\mathrm{Cu}}^{3+}$content

The moles of ${\mathrm{S}}_2{\mathrm{O}}_3^{2-}$in experiment A is 4.55mmol , while the moles of ${\mathrm{S}}_2{\mathrm{O}}_3^{2-}$in experiment B is 5.68 mmol. So, the difference is:

$\mathrm{n}\left(\mathrm{S\_O\_}{3}^{2-}\right)=(5.68-4.55)\mathrm{mmol}=1.13\mathrm{mmol}$

1mol of ${\mathrm{S}}_2{\mathrm{O}}_3^{2-}$equals to 1mol of ${\mathrm{Cu}}^{3+}$. So, the moles of ${\mathrm{Cu}}^{3+}$are:

$$\begin{gathered} \mathrm{now},\mathrm{we}\mathrm{find}\mathrm{x}\mathrm{in}\mathrm{the}\mathrm{formula}{\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{\mathrm{x}}.\mathrm{We}\mathrm{know}\mathrm{that}\mathrm{the}\mathrm{moles}\mathrm{of}{\mathrm{Cu}}^{3+}\mathrm{in}{\mathrm{theYBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-\mathrm{z}}\mathrm{is}1-2\mathrm{z} \\ \mathrm{We}\mathrm{need}\mathrm{to}\mathrm{compare}\mathrm{moles}\mathrm{of}{\mathrm{Cu}}^{3+}\mathrm{with}\mathrm{moles}\mathrm{of}\mathrm{superconductor}\mathrm{to}\mathrm{get}\mathrm{the}\mathrm{number}\mathrm{of}\mathrm{O}\mathrm{atoms}\mathrm{in}\mathrm{the}\mathrm{formula}: \\ \frac{\mathrm{n}\left({\mathrm{Cu}}^{3+}\right)}{\mathrm{n}(\mathrm{superconductor})}=1-2\mathrm{z}=\frac{1.13.{10}^{-3}\mathrm{mol}}{{\displaystyle \frac{1\mathrm{g}}{(666.246-15.9994\mathrm{z})\mathrm{g}/\mathrm{mol}}}}\left(2\right) \\ 1-2\mathrm{z}=0.753-0.018\mathrm{z} \\ \mathrm{the}\mathrm{z}\mathrm{is}: \\ 1.982\mathrm{z}=0.247 \\ \mathrm{z}=\frac{0.247}{1.982}=0.125 \\ \mathrm{the}\mathrm{number}\mathrm{of}\mathrm{O}\mathrm{atoms}\mathrm{in}\mathrm{formula}\mathrm{is}: \\ 7-\mathrm{z}=7-0.125=6.875 \\ \mathrm{So},\mathrm{the}\mathrm{formula}\mathrm{is}{\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6.875}. \\ \mathrm{Therefore}\mathrm{the}\mathrm{value}\mathrm{of}\mathrm{z}\mathrm{in}\mathrm{the}\mathrm{formula}\mathrm{is}0.125. \end{gathered}$$

b) In this task, we need to calculate uncertainty of number of O atoms.

We know that the moles of ${\mathrm{S}}_2{\mathrm{O}}_3^{2-}$in experiment A is $4.55 \pm 0.10 \mathrm{mmol}$, while the moles of ${\mathrm{S}}_2{\mathrm{O}}_3^{2-}$in experiment B is $5.68\pm 0.05\mathrm{mmol}$per gram of$YB{a}_{2}C{u}_3{O}_{7-z}$.

So, we calculate uncertainty using the moles of ${\mathrm{Cu}}^{3+}$ (difference in ${\mathrm{S}}_2{\mathrm{O}}_3^{2-}$required between experiments B and A) and moles of superconductor:

$$\begin{gathered} 1-2\mathrm{z}=\frac{(5.68\pm 0.05-4.55\pm 0.10).{10}^{-3}}{{\displaystyle \frac{1}{666.246-999\mathrm{z}}}}\left(3\right) \\ 1-2\mathrm{z}=\frac{1.13\pm 0.112.{10}^{-3}}{{\displaystyle \frac{1}{666.246-15.9994\mathrm{z}}}} \\ 1-2\mathrm{z}=0.75286\pm 0.07449-(0.018079\pm 0.001789).\mathrm{z} \\ 0.247124\pm 0.074489=1.98192\pm 0.00179.\mathrm{z} \\ =0.125\pm 0.038 \end{gathered}$$

Note that for multiplication, we multiply the uncertainty by the same exact number. For addition and subtraction we use standard deviations to calculate uncertainty:

Therefore the uncertainty of x in the formula is $\sqrt{{\left(s_1\right)}^2+{\left(s_2\right)}^2...}$