# Tutor profile: Christi K.

## Questions

### Subject: Chemistry

Balance the following redox reaction in basic solution: $$ O_{2} $$ + $$ Cr^{3+} $$ --> $$ H_{2}O_{2} $$ + $$ Cr_{2}O_{7}^{2-} $$

1)First we need to divide the redox reaction into half reactions: Reduction: $$ O_{2} $$ ---> $$ H_{2}O_{2} $$ Oxidation: $$ Cr^{3+} $$ ---> $$ Cr_{2}O_{7}^{2-} $$ 2) Next we need to balance everything except oxygen and hydrogen by using coefficients. Reduction: $$ O_{2} $$ ---> $$ H_{2}O_{2} $$ Oxidation: $$ 2Cr^{3+} $$ ---> $$ Cr_{2}O_{7}^{2-} $$ 3) Then balance oxygen by adding water as needed. Reduction: $$ O_{2} $$ ---> $$ H_{2}O_{2} $$ Oxidation: $$ 2Cr^{3+} $$ + $$ 7H_{2}O $$ --> $$ Cr_{2}O_{7}^{2-} $$ 4) Then balance hydrogen by adding $$ H^{+} $$ as needed. Reduction: $$ O_{2} $$ + $$ 2H^{+} $$ ---> $$ H_{2}O_{2} $$ Oxidation: $$ 2Cr^{3+} $$ + $$ 7H_{2}O $$ --> $$ Cr_{2}O_{7}^{2-} $$ + $$ 14H^{+} $$ 5) Next, we balance the charges on each side by adding the appropriate number of electrons. For the reduction reaction, there is a total charge of +2 on the reactants side and a charge of 0 on the products side, so we need to add 2 electrons to the reactants side in order for the charges to balance. For the oxidation reaction, there is a total charge of +6 on the reactants side and a total charge of +12 on the products side, so 6 electrons must be added to the products side. Reduction: $$ O_{2} $$ + $$ 2H^{+} $$ + $$ 2e^{-} $$ ---> $$H_ {2}O_{2} $$ Oxidation: $$ 2Cr^{3+} $$ + $$ 7H_{2}O $$ --> $$ Cr_{2}O_{7}^{2-} $$ + $$ 14H^{+} $$ + $$ 6e^{-} $$ 6) in order to be able to recombine the half reactions, we must have the same number of electrons exchanged in each reaction. We can do this by multiplying the entire reduction reaction by 3 so that a total of 6 electrons are exchanged. Reduction: $$ 3O_{2} $$ + $$ 6H^{+} $$ + $$ 6e^{-} $$ ---> $$ 3H_{2}O_{2} $$ Oxidation: $$ 2Cr^{3+} $$ + $$ 7H_{2}O $$ --> $$ Cr_{2}O_{7}^{2-} $$ + $$ 14H^{+} $$ + $$ 6e^{-} $$ 7)The reactions can now be recombined. Be sure to simplify any compounds that appear on both the reactant and products sides. For example, there are 6H+ on the reactants side and 14H+ on the products side. We simplify this to show only 8H+ on the products side. $$ 3O_{2} $$ + $$ 2Cr^{3+} $$ + $$ 7H_{2}O $$ ---> $$ 3H_{2}O_{2} $$ + $$ 8H^{+} $$ + $$ Cr_{2}O_{7}^{2-} $$ 8) Since the problem asked us to balance the equation in basic solution, we need to reflect that by adding OH- ions to each side to neutralize any H+ and create water. Adding OH- : $$ 3O_{2} $$ + $$ 2Cr^{3+} $$ + $$ 7H_{2}O $$ + $$ 8OH^{-} $$ ---> $$ 3H_{2}O_{2} $$ + $$ 8H^{+} $$ +$$ 8OH^{-} $$ + $$ Cr_{2}O_{7}^{2-} $$ Creates water: $$ 3O_{2} $$ + $$ 2Cr^{3+} $$ + $$ 7H_{2}O $$ + $$ 8OH^{-} $$ ---> $$ 3H_{2}O_{2} $$ + $$ 8H_{2}O $$ + $$ Cr_{2}O_{7}^{2-} $$ 9)Since water is now present on both sides of the reaction, reduce it to show only 1 water molecule on the products side: $$ 3O_{2} $$ + $$ 2Cr^{3+} $$ + $$ 8OH^{-} $$ ---> $$ 3H_{2}O_{2} $$ + $$ H_{2}O $$ + $$ Cr_{2}O_{7}^{2-} $$ 10) Check your answer to make sure both the atoms and charge are balanced: Totals: Reactants Products Oxygen 14 14 Chromium 2 2 Hydrogen 8 8 Total charge -2 -2 If all numbers match, then your equation is balanced!

### Subject: Biology

Rabbit’s ears can be either short or floppy, where short ears are dominant over floppy ears. There are 653 individuals in a population. 104 rabbits have floppy ears and 549 have short ears. Find: the frequency of the dominant and recessive alleles and the frequency of individuals with dominant, heterozygous, and recessive genotypes.

To solve this problem, we must use the Hardy Weinberg Principle. This involves using two equations: The first equation helps us to determine the frequency of the alleles in the population. It is as follows: p + q = 1, where p is the frequency of the dominant allele and q is the frequency of the recessive allele. The second equation helps us to determine the frequency of individuals in the population. It is as follows: p^2 + 2pq + q^2 = 1, where p^2 is the frequency of the homozygous dominant individuals, 2pq is the frequency of the heterozygous individuals, and q^2 is the frequency of the homozygous recessive individuals. Since the allele for floppy ears is recessive, all 104 rabbits with floppy ears must be homozygous recessive. q^2 represents the frequency of the homozygous recessive individuals. To determine this frequency, we need to divide the 104 rabbits by the total of 653. q^2 = 104/653 q^2 = 0.16 This means that 16% of the population is homozygous recessive and has floppy ears. We can then use this information to solve for q, the frequency of the recessive allele. q = square root of q^2, so q = square root of 0.16 q = 0.4 This means that 40% of the alleles in the population are recessive. Using this information, we can determine that the other 60% of the alleles are dominant. We can use the following calculation: p + q = 1 p + 0.4 = 1 p = 0.6 Now that we know the values of both p and q, we can calculate the frequencies of homozygous dominant and heterozygous individuals. Since p^2 represents the frequency of homozygous dominant individuals, we can substitute 0.6 for p and solve: p^2 =0.6^2 = 0.36 This means that 36% of the rabbits in the population are heterozygous dominant for their short ears. Since 2pq represents the frequency of heterozygous individuals, we can substitute 0.6 for p and 0.4 for q and solve: 2pq = 2 * 0.6 * 0.4 = 0.48 This means that 48% of the rabbits in the population are heterozygous for their short ears.

### Subject: Physical Science

A skateboarder tries to skateboard up a hill. He slides forward 2 meters, then slips back 1 meter, then slides forward again 3 meters, finally reaching the top of the hill. What distance has the skateboarder traveled? What is his displacement?

Distance and displacement are different. The distance the skateboarder has traveled is the sum of all the movements he made. His displacement, however, is the distance he is from his starting point. To calculate his distance, we simply add 2 meters + 1 meter + 3 meters for a total of 6 meters traveled. To calculate his displacement, we must assign positive and negative directions to his movements and then take the sum. All movements up the hill will be designated positive and movements back down the hill will be designated negative. Our calculation will look like this: He slides forward 2 meters (+2) meters He slips back 1 meter + (-1) meters He slides forward 3 meters + (+3) meters Total = 4 meters

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