Question

1. write a balanced equation for the reaction of kmno₄ with h₂o₂ in the presence of h₂so₄.
2. calculate the number of moles of kmno₄ for each titer value.
3. calculate the number of moles of h₂o₂ for each trial.
4. calculate the grams of h₂o₂ for each trial (to 0.001g).
5. calculate the mass percent of h₂o₂ for each trial.
6. use the six values for the grams of h₂o₂ and do a q - test.

• if any datum should be rejected based on simple statistical probability because it might be too much “off” to be useful, then a statistical tool called a q - test is done.

1. determine the mean using the surviving data.

• the mean or average indicates the central number around which the data points appear to cluster. only use the data that survives the q - test.

1. calculate the standard deviation of your surviving data.

• the standard deviation is an estimate of the scattering from the average. this is also a measure of precision. higher the precision of your data, the smaller the standard deviation.

Explanation:

Step1: Write balanced chemical equation

The reaction is a redox - reaction. The balanced equation is $2KMnO_4 + 5H_2O_2+ 3H_2SO_4=K_2SO_4 + 2MnSO_4+ 5O_2\uparrow+ 8H_2O$.

Step2: Calculate moles of $KMnO_4$

If we know the volume ($V$ in L) and molarity ($M$) of $KMnO_4$ solution used in titration, we use the formula $n = M\times V$, where $n$ is the number of moles.

Step3: Calculate moles of $H_2O_2$

From the balanced equation, the mole - ratio of $KMnO_4$ to $H_2O_2$ is $2:5$. So, $n_{H_2O_2}=\frac{5}{2}n_{KMnO_4}$, where $n_{H_2O_2}$ is the number of moles of $H_2O_2$ and $n_{KMnO_4}$ is the number of moles of $KMnO_4$.

Step4: Calculate grams of $H_2O_2$

The molar mass of $H_2O_2$ is $M_{H_2O_2}=(2\times1 + 2\times16)=34\ g/mol$. The mass $m = n\times M$, so $m_{H_2O_2}=n_{H_2O_2}\times34\ g/mol$.

Step5: Calculate mass - percent of $H_2O_2$

If the mass of the sample is $m_{sample}$, the mass - percent of $H_2O_2$ is $\text{Mass}\%=\frac{m_{H_2O_2}}{m_{sample}}\times100\%$.

Step6: Q - test

Arrange the data in ascending order: $x_1,x_2,\cdots,x_n$. Calculate $Q_{calculated}=\frac{\vert x_{suspect}-x_{nearest}\vert}{x_{max}-x_{min}}$. Compare $Q_{calculated}$ with the critical $Q$ - value (from $Q$ - tables) for the given number of data points and confidence level. If $Q_{calculated}>Q_{critical}$, reject the suspect data point.

Step7: Calculate the mean

If the remaining data points are $x_1,x_2,\cdots,x_m$, the mean $\bar{x}=\frac{\sum_{i = 1}^{m}x_i}{m}$.

Step8: Calculate the standard deviation

The formula for the standard deviation $s=\sqrt{\frac{\sum_{i = 1}^{m}(x_i-\bar{x})^2}{m - 1}}$.

Since no specific values for volume, molarity, mass of sample etc. are given, we cannot provide numerical answers. But the above steps show the general method for solving each part of the problem.

Answer:

Step1: Write balanced chemical equation

The reaction is a redox - reaction. The balanced equation is $2KMnO_4 + 5H_2O_2+ 3H_2SO_4=K_2SO_4 + 2MnSO_4+ 5O_2\uparrow+ 8H_2O$.

Step2: Calculate moles of $KMnO_4$

If we know the volume ($V$ in L) and molarity ($M$) of $KMnO_4$ solution used in titration, we use the formula $n = M\times V$, where $n$ is the number of moles.

Step3: Calculate moles of $H_2O_2$

From the balanced equation, the mole - ratio of $KMnO_4$ to $H_2O_2$ is $2:5$. So, $n_{H_2O_2}=\frac{5}{2}n_{KMnO_4}$, where $n_{H_2O_2}$ is the number of moles of $H_2O_2$ and $n_{KMnO_4}$ is the number of moles of $KMnO_4$.

Step4: Calculate grams of $H_2O_2$

The molar mass of $H_2O_2$ is $M_{H_2O_2}=(2\times1 + 2\times16)=34\ g/mol$. The mass $m = n\times M$, so $m_{H_2O_2}=n_{H_2O_2}\times34\ g/mol$.

Step5: Calculate mass - percent of $H_2O_2$

If the mass of the sample is $m_{sample}$, the mass - percent of $H_2O_2$ is $\text{Mass}\%=\frac{m_{H_2O_2}}{m_{sample}}\times100\%$.

Step6: Q - test

Arrange the data in ascending order: $x_1,x_2,\cdots,x_n$. Calculate $Q_{calculated}=\frac{\vert x_{suspect}-x_{nearest}\vert}{x_{max}-x_{min}}$. Compare $Q_{calculated}$ with the critical $Q$ - value (from $Q$ - tables) for the given number of data points and confidence level. If $Q_{calculated}>Q_{critical}$, reject the suspect data point.

Step7: Calculate the mean

If the remaining data points are $x_1,x_2,\cdots,x_m$, the mean $\bar{x}=\frac{\sum_{i = 1}^{m}x_i}{m}$.

Step8: Calculate the standard deviation

The formula for the standard deviation $s=\sqrt{\frac{\sum_{i = 1}^{m}(x_i-\bar{x})^2}{m - 1}}$.

Since no specific values for volume, molarity, mass of sample etc. are given, we cannot provide numerical answers. But the above steps show the general method for solving each part of the problem.