$$a. H_2O_2 + b. KMnO_4 + c. H_2SO_4 \to d. K_2SO_4 + e. MnSO_4 + f. H_2O + g. O_2$$
Select the correct answer from the codes given below :
Balancing the Chemical Equation
The goal is to find the stoichiometric coefficients ($a, b, c, d, e, f, g$) that correctly balance the given chemical equation:
$a. H_2O_2 + b. KMnO_4 + c. H_2SO_4 \to d. K_2SO_4 + e. MnSO_4 + f. H_2O + g. O_2$This is a redox reaction where $H_2O_2$ is oxidized and $KMnO_4$ is reduced in an acidic medium ($H_2SO_4$). We will check the atom balance using the coefficients from the correct option.
Checking Stoichiometric Coefficients
Let's test the coefficients provided in Option B: $a=1, b=2, c=3, d=1, e=2, f=4, g=3$.
Substituting these values into the equation gives:
$1 H_2O_2 + 2 KMnO_4 + 3 H_2SO_4 \to 1 K_2SO_4 + 2 MnSO_4 + 4 H_2O + 3 O_2$Atom Balance Verification
We verify the number of atoms for each element on both the reactant (left) and product (right) sides.
| Element | Reactant Side | Product Side | Balanced? |
|---|---|---|---|
| K | $2 \times 1 = 2$ | $1 \times 2 = 2$ | Yes |
| Mn | $2 \times 1 = 2$ | $2 \times 1 = 2$ | Yes |
| S | $3 \times 1 = 3$ | $(1 \times 1) + (2 \times 1) = 1 + 2 = 3$ | Yes |
| H | $(1 \times 2) + (3 \times 2) = 2 + 6 = 8$ | $4 \times 2 = 8$ | Yes |
| O | $(1 \times 2) + (2 \times 4) + (3 \times 4) = 2 + 8 + 12 = 22$ | $(1 \times 4) + (2 \times 4) + (4 \times 1) + (3 \times 2) = 4 + 8 + 4 + 6 = 22$ | Yes |
All elements are balanced with the coefficients $a=1, b=2, c=3, d=1, e=2, f=4, g=3$.
Important Questions from Hypothesis testing - Teaching
- The null hypothesis in nonparametric test often _______.
1. Includes specification of a population's parameters
2. Is used to evaluate some general population aspect
3. Is very similar to that used in regression analysis
4. Simultaneously tests more than two population parameters - The _______ test determines whether there is a significant difference between the observed and hypothesized distribution for a sample.
1. Independence
2. Coefficient of determination
3. Correlation analysis
4. Goodness-of-fit - Match the LIST-I with LIST-II
LIST-I LIST-II A. One-Tailed Test I. Null hypothesis is rejected if the sample value is significantly higher or lower than the hypothesized value of the population parameter B. Paired difference Test II. A hypothesis test of the difference between the sample means of two independent samples C. Two-Tailed Test III. A sample value significantly above the hypothesized population value will lead to rejection of the null hypothesis D. Upper-Tailed Test IV. Concerned only with whether the observed value deviates from the hypothesized value in one direction
Choose the correct answer from the options given below: - The null hypothesis that all slope coefficients are simultaneously equal to zero is tested in logit model by:
- Arrange in correct sequence the steps for testing Statistical Hypothesis :
I. A random sample is drawn from population.
II. Specify the level of significance.
III. Value of the sample statistic is obtained.
IV. Obtained sample statistic is examined with the random sampling distribution of the statistic under consideration.
V. Formulate Null Hypothesis about a parameter of the population, along with an alternate hypothesis.
VI. Retain Null Hypothesis if particular sample outcome is in line with the expected outcomes, otherwise reject it and retain alternate hypothesis.
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