# Tutor profile: Dirk M.

## Questions

### Subject: Chemistry

In the following reaction: $$N_2$$ + $$3H_2$$ = $$2NH_3$$ How many grams of Hydrogen is needed to completely react with 7 grams of Nitrogen?

From the Periodic table, we find that 1 mole of $$N_2$$ has a mass of 28 g. i.e. ( 2 N x 14.0 g/mole = 28 g/mole $$N_2$$) We also know that 1 mole of $$H_2$$ is 2.02 g/mole i.e. (2 H x 1.01 g/mole = 2.02 g/mole $$H_2$$) The mole ration from the balanced equation shows: 1:3:2 $$N_2$$: $$H_2$$: $$NH_3$$ Step 1: Convert the mass of Nitrogen to moles using the mole-mass conversion equation (Mole = mass/molar mass) X mole $$N_2$$ = 7 g $$N_2$$ / 28 g/mole $$N_2$$ = 0.25 mol $$N_2$$ Step 2: Using the mole ratio from the balanced equation, 1:3 $$N_2$$: $$H_2$$, we can convert the know number of $$N_2$$ moles to the required number of $$H_2$$ moles. 0.25 mole $$N_2$$ x (3 mole $$H_2$$) / (1 mole $$N_2$$) = 0.75 mole $$H_2$$ We now know the number of moles of $$H_2$$ needed to completely react with $$N_2$$ Step 3: Convert the number of moles of $$H_2$$ to mass. 0.75 mole $$H_2$$ x 2.02 g/mole $$H_2$$ = 1.51 grams of $$H_2$$ A quicker way to complete this calculation would be to do all calculations in one step: Our ratio is: 7 g $$N_2$$ / 28 g/mole $$N_2$$ = (X)/(3 moles)(2.02 g/mole $$H_2$$). Cross multiply and the answer is 1.52 g $$H_2$$. {X = (7 g $$N_2$$)(3 moles)(2.02 g/mole $$H_2$$)/ 28 g/mole $$N_2$$ = 1.51 g $$H_2$$}

### Subject: Basic Chemistry

Propane is a gas used for cooking and heating. Use the mole concept to calculate the number of atoms in 2.12 mol of propane ($$C_3H_8$$).

1) Analyze: List the knows and unknown. Knowns: Number of moles = 2.12 mol $$C_3H_8$$ 1 mol $$C_3H_8$$ = 6.02 X $$10^{23}$$ molecules $$C_3H_8$$ ( Avogadro’s numbers) 1 mol $$C_3H_8$$ = 11 atoms (3 Carbon atoms and 8 Hydrogen atoms) Unknown: The number of atoms in 2.12 mol $$C_3H_8$$ 2) Calculate: solve the unknown. (6.02 X $$10^{23}$$ molecules $$C_3H_8$$)/(1 mol $$C_3H_8$$) (conversion factor from mole to molecule) (11 atoms) / (1 molecule $$C_3H_8$$) (conversion factor from molecules to atoms) (2.12 mol $$C_3H_8$$) x (6.02 X $$10^{23}$$ molecules $$C_3H_8$$)/(1 mol $$C_3H_8$$) x (11 atoms) / (1 molecule $$C_3H_8$$) Therefore, We are left with the following: 2.12 x 6.02 X $$10^{23}$$ x11 = 1.4 x $$10^{25}$$ Atoms in 2.12 mol $$C_3H_8$$

### Subject: Biology

Allele Frequency The Hardy-Weinberg principle can be used to predict the frequencies of certain genotypes if you know the frequency of other genotypes. Imagine, for example, that you know of a genetic condition, controlled by two alleles S and s, that follows the rule of simple dominance at a single locus. The condition affects only homozygous recessive individuals. (The heterozygous phenotype shows no symptoms.) The population you are studying has a population size of 10,000, and there are 36 individuals affected by the condition ($$q^2$$ = 0.0036). Based on this information, use the Hardy-Weinberg equations to answer the following questions: 1. Calculate: What are the frequencies of the S and s alleles? 2. Calculate: What are the frequencies of the SS, Ss, and ss genotypes? 3. Calculate: What percentage of people, in total, are likely to be carrying the s allele, whether or not they know it?

The Hardy-Weinberg principle states that allele frequencies in a population should remain constant unless one or more factors cause those frequencies to change. The principle makes predictions like Punnett squares- but for populations, not individuals. Suppose that there are two alleles for a gene: A (dominant) and a (recessive). A cross of these alleles can produce three possible genotypes: AA, Aa, and aa. The frequencies of genotypes in the population can be predicted by these equations, where p and q are the frequencies of the dominant and recessive alleles: In symbols: $$p^2$$ + 2pq +$$q^2$$ = 1 and p + q = 1 In words: (frequency of AA) + (frequency of Aa) + (frequency of aa) = 100% And (frequency of A) + (frequency of a) = 100% 1. Calculate: What are the frequencies of the S and s alleles? From the question we know that $$q^2$$ = 0.0036 therefore, we can calculate q: q = $$sqrt(0.0036)$$ = 0.06 x 100 = 6% - According to the Hardy-Weinberg principle, we have the equation: p + q = 1. Therefore: p + 0.06 = 1 and p = 1 – 0.06 = 0.94 or = 94% Since q stands for homozygous recessive individuals, and p stands for homozygous dominant individuals, the frequency of the s allele is 0.06 or (6%) and the frequency of the S allele is 0.94 or (94%) 2. Calculate: What are the frequencies of the SS, Ss, and ss genotypes? - According to the Hardy-Weinberg principle, we have another equation to identify the frequency of other genotypes: $$q^2$$ + 2qp + $$p^2$$ = 1 $$(0.94)^2$$ + 2 (0.94) (0.06) + $$(0.06)^2$$ = 1 Therefore: $$p^2$$ = 0.8836 = 88.36% $$q^2$$ = 0.0036 = 0.36% 2pq = 0.1128 = 11.28% Since $$p^2$$ stands for homozygous dominant individuals, it represents the SS genotypes. Since $$q^2$$ stands for homozygous recessive individuals, it represents the ss genotypes. Since 2pq stands for heterozygous individuals, it represents the Ss genotypes. Therefore, the frequency of the SS genotypes is 88.36%, the frequency of the ss genotypes is 0.36%, and the frequency of the Ss genotypes is 11.28%. 3. Calculate: What percentage of people, in total, are likely to be carrying the s allele, whether or not they know it? There are two groups that carrying the s allele, the homozygous recessive group $$(q^2)$$ and the heterozygous group (2pq). Even though the heterozygous group does not express the s allele (recessive allele), which means it does not know it (since the dominant alleles are much stronger). Hence, the percentage of people, in total, is likely to be carrying the s allele is: $$q^2$$ + 2pq = 11.28% + 0.36% = 11.64%

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