Some catalytic converters in automobiles contain two...

Some catalytic converters in automobiles contain two manganese oxides: $\mathrm{Mn}_{2} \mathrm{O}_{3}$ and $\mathrm{MnO}_{2}.$ a. What are the names of these compounds? b. What is the manganese content of each (expressed as a percent by mass)? c. Explain how $\mathrm{Mn}_{2} \mathrm{O}_{3}$ and $\mathrm{MnO}_{2}$ are consistent with the law of multiple proportions.

Some catalytic converters in automobiles contain two manganese oxides: $\mathrm{Mn}_{2} \mathrm{O}_{3}$ and $\mathrm{MnO}_{2}.$
a. What are the names of these compounds?
b. What is the manganese content of each (expressed as a percent by mass)?
c. Explain how $\mathrm{Mn}_{2} \mathrm{O}_{3}$ and $\mathrm{MnO}_{2}$ are consistent with the law of multiple proportions.

Key Concepts

Chemical Nomenclature

Chemical nomenclature in inorganic chemistry involves assigning systematic names to compounds based on the elements present and their oxidation states. For example, metal oxides are typically named by recognizing the metal's oxidation state when more than one is possible, often using Roman numerals. This allows clear differentiation between compounds containing the same elements in different ratios or oxidation states.

Percent Composition

Percent composition is a method used to calculate the mass percentage of each element in a compound. This involves determining the mass of each element present in one mole of the compound and dividing by the total molar mass, then multiplying by 100 to get a percentage. This concept is crucial for analyzing chemical formulas and understanding the relative amounts of elements in compounds.

Law of Multiple Proportions

The law of multiple proportions states that when two elements form more than one compound, the masses of the second element that combine with a fixed mass of the first element are in the ratio of small whole numbers. This principle supports the idea that chemical compounds form in definite proportions and provides evidence for the existence of discrete chemical species, as demonstrated by comparing different oxide compounds of a single metal.

Transcript

00:01 Okay, so for this question, they want us to name these two compounds, and then they want us to find the percent mass of manganese in these compounds.

00:08 And then lastly, they want us to prove that these two compounds follow the law of multiple proportions.

00:16 Right? so, manganese has multiple oxidative states, right? so the oxidative states are plus two, plus three, plus four, and plus seven.

00:29 Right okay so the first thing we do is we find the charge on oxygen so oxygen always has a negative 2 oxidative state right so negative 2 and since we have 3 we need to multiply this by 3 that means 03 has a negative 6 charge so in order to even it out we have 2 manganese here right so that means each manganese needs to have a plus 3 charge because if each manganese has a plus 3 charge and we have two of them we get plus 6 and these two charges from the oxygen and from the manganese will cancel out right so we have it will be manganese or plus 3 so 1 2 3 oxide now for this one oxygen has a negative 2 oxidative say like always but we have 2 oxygen that means 2 times negative 2 will equal negative 4 so that means since really 1 manganese i mean this manganese must be a plus four charge to cancel out the charge from this negative four here.

01:40 So it will be manganese, room and number four oxide.

01:52 Now for the next part, they want us to find the percent composition of manganese.

01:57 So the first thing that we should do is we have to find the total atomic weight of manganese 3 oxide.

02:08 So, manganese has a molecular weight of 55, since we have two of them, we've got to multiply it by 2, plus oxygen, we have 3 multiplied by 16 since the molecular weight of oxygen is 16.

02:23 This gives us 158.

02:27 Now we do manganese, which is 55, and we have two of them divided by 158 times it by 100, and we get about 69 .62%...

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