Question

for the following reaction, 3.59 grams of tetraphosphorus decaoxide are mixed with excess perchloric acid (hclo4). the reaction yields 4.59 grams of phosphoric acid. perchloric acid (hclo4)(aq) + tetraphosphorus decaoxide (s) → phosphoric acid (aq) + dichlorine heptaoxide (l) what is the theoretical yield of phosphoric acid? grams what is the percent yield of phosphoric acid? %

Explanation:

Step1: Write the balanced chemical equation

The balanced chemical equation for the reaction of tetraphosphorus decaoxide ($P_4O_{10}$) with perchloric acid ($HClO_4$) to form phosphoric acid ($H_3PO_4$) and dichlorine heptaoxide ($Cl_2O_7$) is:
$P_4O_{10}+12HClO_4 = 4H_3PO_4 + 6Cl_2O_7$

Step2: Calculate the molar mass of $P_4O_{10}$

The molar mass of $P_4O_{10}$: $M_{P_4O_{10}}=(4\times30.97 + 10\times16.00)\text{ g/mol}=283.88\text{ g/mol}$

Step3: Calculate the moles of $P_4O_{10}$

Given the mass of $P_4O_{10}$ is $m = 3.59\text{ g}$. The number of moles of $P_4O_{10}$, $n_{P_4O_{10}}=\frac{m}{M}=\frac{3.59\text{ g}}{283.88\text{ g/mol}}\approx0.0127\text{ mol}$

Step4: Determine the mole - ratio of $P_4O_{10}$ to $H_3PO_4$

From the balanced equation, the mole - ratio of $P_4O_{10}$ to $H_3PO_4$ is $1:4$. So the moles of $H_3PO_4$ produced theoretically, $n_{H_3PO_4}=4\times n_{P_4O_{10}} = 4\times0.0127\text{ mol}=0.0508\text{ mol}$

Step5: Calculate the molar mass of $H_3PO_4$

The molar mass of $H_3PO_4$: $M_{H_3PO_4}=(3\times1.01+30.97 + 4\times16.00)\text{ g/mol}=97.994\text{ g/mol}$

Step6: Calculate the theoretical yield of $H_3PO_4$

The theoretical yield of $H_3PO_4$, $m_{theoretical}=n_{H_3PO_4}\times M_{H_3PO_4}=0.0508\text{ mol}\times97.994\text{ g/mol}\approx4.98\text{ g}$

Step7: Calculate the percent yield

The actual yield of $H_3PO_4$ is $m_{actual}=4.59\text{ g}$. The percent yield, $\text{Percent Yield}=\frac{m_{actual}}{m_{theoretical}}\times100\%=\frac{4.59\text{ g}}{4.98\text{ g}}\times100\%\approx92.2\%$

Answer:

The theoretical yield of phosphoric acid is approximately $4.98$ grams and the percent yield is approximately $92.2\%$