Question

Calculate the percentage by mass of the indicated element in the following compounds: (a) carbon in acetylene, \(\mathrm{C}_{2} \mathrm{H}_{2}\), a gas used in welding; (b) hydrogen in ascorbic acid, \(\mathrm{HC}_{6} \mathrm{H}_{7} \mathrm{O}_{6}\), also known as vitamin \(\mathrm{C}\); (c) hydrogen in ammonium sulfate, \(\left(\mathrm{NH}_{4}\right)_{2} \mathrm{SO}_{4}\), a substance used as a nitrogen fertilizer; (d) platinum in \(\mathrm{PtCl}_{2}\left(\mathrm{NH}_{3}\right)_{2}\), a chemotherapy agent called cisplatin; (e) oxygen in the female sex hormone estradiol, \(\mathrm{C}_{18} \mathrm{H}_{24} \mathrm{O}_{2}\); (f) carbon in capsaicin, \(\mathrm{C}_{18} \mathrm{H}_{27} \mathrm{NO}_{3}\), the compound that gives the hot taste to chili peppers.

Short answer

(a) The percentage of Carbon in Acetylene, \(\mathrm{C}_{2} \mathrm{H}_{2}\), is approximately 92.27%. (b) The percentage of Hydrogen in Ascorbic Acid, \(\mathrm{HC}_{6}\mathrm{H}_{7}\mathrm{O}_{6}\), is approximately 4.58%. (c) The percentage of Hydrogen in Ammonium Sulfate, \(\left(\mathrm{NH}_{4}\right)_{2}\mathrm{SO}_{4}\), is approximately 6.11%. (d) The percentage of Platinum in \(\mathrm{PtCl}_{2}\left(\mathrm{NH}_{3}\right)_{2}\), is approximately 65.02%. (e) The percentage of Oxygen in Estradiol, \(\mathrm{C}_{18}\mathrm{H}_{24}\mathrm{O}_{2}\), is approximately 11.77%. (f) The percentage of Carbon in Capsaicin, \(\mathrm{C}_{18} \mathrm{H}_{27} \mathrm{NO}_{3}\), is approximately 70.59%.

Step-by-step solution

(a) Calculate the percentage of Carbon in Acetylene, \(\mathrm{C}_{2} \mathrm{H}_{2}\)

First, determine the molar mass of Carbon (C) and Hydrogen (H). For Carbon, the molar mass is 12.01 g/mol, and for Hydrogen, it is 1.008 g/mol. Then, calculate the molar mass of \(\mathrm{C}_{2} \mathrm{H}_{2}\): Molar mass of \(\mathrm{C}_{2} \mathrm{H}_{2}\) = (2 * molar mass of C) + (2 * molar mass of H)= (2*12.01) g/mol + (2*1.008) g/mol = 26.036 g/mol Now, calculate the percentage of Carbon in Acetylene: % C = (Total mass of Carbon in the compound / Molar mass of the compound) * 100 = (2 * 12.01 g/mol) / 26.036 g/mol * 100 ≈ 92.27 %

(b) Calculate the percentage of Hydrogen in Ascorbic Acid, \(\mathrm{HC}_{6}\mathrm{H}_{7}\mathrm{O}_{6}\)

Determine the molar mass of Oxygen (O), which is 16.00 g/mol. Then, calculate the molar mass of \(\mathrm{HC}_{6}\mathrm{H}_{7}\mathrm{O}_{6}\): Molar mass of \(\mathrm{HC}_{6}\mathrm{H}_{7}\mathrm{O}_{6}\)= (1 * molar mass of H) + (6 * molar mass of C) + (7 * molar mass of H) + (6 * molar mass of O)= 1.008 g/mol + (6*12.01) g/mol + (7*1.008) g/mol + (6*16.00) g/mol = 176.124 g/mol Now, calculate the percentage of Hydrogen in Ascorbic Acid: % H = (Total mass of Hydrogen in the compound / Molar mass of the compound) * 100 = (8 * 1.008 g/mol) / 176.124 g/mol * 100 ≈ 4.58 %

(c) Calculate the percentage of Hydrogen in Ammonium Sulfate, \(\left(\mathrm{NH}_{4}\right)_{2}\mathrm{SO}_{4}\)

Determine the molar mass of Nitrogen (N) and Sulfur (S). Nitrogen has a molar mass of 14.01 g/mol, and Sulfur has a molar mass of 32.07 g/mol. Then, calculate the molar mass of \(\left(\mathrm{NH}_{4}\right)_{2}\mathrm{SO}_{4}\): Molar mass of \(\left(\mathrm{NH}_{4}\right)_{2}\mathrm{SO}_{4}\)= (2 * ((1 * molar mass of N) + (4 * molar mass of H))) +(1 * molar mass of S) + (4 * molar mass of O)= 2*( 14.01 g/mol + (4*1.008) g/mol )+ 32.07 g/mol + (4*16.00) g/mol = 132.14 g/mol Now, calculate the percentage of Hydrogen in Ammonium Sulfate: % H = (Total mass of Hydrogen in the compound / Molar mass of the compound) * 100 = (8 * 1.008 g/mol) / 132.14 g/mol * 100 ≈ 6.11 %

(d) Calculate the percentage of Platinum in \(\mathrm{PtCl}_{2}\left(\mathrm{NH}_{3}\right)_{2}\)

Determine the molar mass of Platinum (Pt) and Chlorine (Cl). Platinum has a molar mass of 195.08 g/mol, and Chlorine has a molar mass of 35.45 g/mol. Then, calculate the molar mass of \(\mathrm{PtCl}_{2}\left(\mathrm{NH}_{3}\right)_{2}\): Molar mass of \(\mathrm{PtCl}_{2}\left(\mathrm{NH}_{3}\right)_{2}\) = (1 * molar mass of Pt) + (2 * molar mass of Cl) + (2 * ((1 * molar mass of N) + (3 * molar mass of H)))= 195.08 g/mol + (2*35.45) g/mol + 2*( 14.01 g/mol + (3*1.008) g/mol ) = 300.05 g/mol Now, calculate the percentage of Platinum in cisplatin: % Pt = (Total mass of Pt in the compound / Molar mass of the compound) * 100 = (1 * 195.08 g/mol) / 300.05 g/mol * 100 ≈ 65.02 %

(e) Calculate the percentage of Oxygen in Estradiol, \(\mathrm{C}_{18}\mathrm{H}_{24}\mathrm{O}_{2}\)

Calculate the molar mass of \(\mathrm{C}_{18}\mathrm{H}_{24}\mathrm{O}_{2}\): Molar mass of \(\mathrm{C}_{18}\mathrm{H}_{24}\mathrm{O}_{2}\)= (18 * molar mass of C) + (24 * molar mass of H) + (2 * molar mass of O)= (18*12.01) g/mol + (24*1.008) g/mol + (2*16.00) g/mol = 272.293 g/mol Now, calculate the percentage of Oxygen in Estradiol: % O = (Total mass of Oxygen in the compound / Molar mass of the compound) * 100 = (2 * 16.00 g/mol) / 272.293 g/mol * 100 ≈ 11.77 %

(f) Calculate the percentage of Carbon in Capsaicin, \(\mathrm{C}_{18} \mathrm{H}_{27} \mathrm{NO}_{3}\)

Determine the molar mass of Nitrogen (N). Then, calculate the molar mass of \(\mathrm{C}_{18} \mathrm{H}_{27} \mathrm{NO}_{3}\): Molar mass of \(\mathrm{C}_{18} \mathrm{H}_{27} \mathrm{NO}_{3}\)= (18 * molar mass of C) + (27 * molar mass of H) + (1 * molar mass of N) + (3 * molar mass of O)= (18*12.01) g/mol + (27*1.008) g/mol + 14.01 g/mol + (3*16.00) g/mol = 305.422 g/mol Now, calculate the percentage of Carbon in Capsaicin: % C = (Total mass of Carbon in the compound / Molar mass of the compound) * 100 = (18 * 12.01 g/mol) / 305.422 g/mol * 100 ≈ 70.59 %

Key concepts

Molar Mass

Understanding molar mass is essential when calculating the percentage by mass of an element in a chemical compound. Molar mass is the weight of one mole of a substance, typically expressed in grams per mole \( g/mol \). It is calculated by summing the atomic masses of all the atoms in a molecule of the compound.
In the case of acetylene \( \mathrm{C}_{2} \mathrm{H}_{2} \), its molar mass is calculated by adding the masses of two carbon atoms and two hydrogen atoms. Similarly, for a more complex molecule like ascorbic acid \( \mathrm{HC}_{6} \mathrm{H}_{7} \mathrm{O}_{6} \), you sum the masses of hydrogen, carbon, and oxygen based on their respective counts within the molecule.
Remember to multiply the atomic masses by the number of each kind of atom present in the compound to get the accurate molar mass. Every element contributes to the total weight, and knowing each allows us to calculate specific percentages by mass.

Chemical Compounds

Chemical compounds are substances formed by the combination of two or more elements in fixed ratios. They have specific formulas that indicate the types and numbers of atoms present. For example, acetylene with the formula \( \mathrm{C}_{2} \mathrm{H}_{2} \) contains two carbon atoms and two hydrogen atoms.
The properties of the compounds are dictated by the arrangement of atoms and the types of chemical bonds holding those atoms together. When analyzing chemical compounds, understanding the formula is crucial because it directly informs the necessary processes for determining aspects like molar mass, and subsequently, percentage by mass.
Each compound has unique characteristics due to its specific composition. For instance, cisplatin \( \mathrm{PtCl}_{2}\left(\mathrm{NH}_{3}\right)_{2} \) is a chemotherapy agent because of its specific platinum, chlorine, nitrogen, and hydrogen composition and arrangement.

Elemental Analysis

Elemental analysis is the process of determining the percentage composition of elements within a chemical compound. This process is often essential for determining the purity of a substance or understanding its composition on a deeper level.
To conduct an elemental analysis, you calculate the mass percentage of a specific element compared to the entire compound. This involves dividing the total mass of the element in the compound by the molar mass of the entire compound, and then multiplying by 100 to get a percentage.
For instance, if you want to find out how much carbon is in capsaicin \( \mathrm{C}_{18} \mathrm{H}_{27} \mathrm{NO}_{3} \), you compare the total mass of the carbon atoms to the molar mass of the compound. This method not only helps chemists to verify empirical formulas but also aids industries in quality control of chemical products by ensuring consistency in elemental composition.