Question

A certain mixture of \(\mathrm{MnO}\) and \(\mathrm{MnO}_{2}\) contains \(66.67\) mol per cent of \(\mathrm{MnO}\). What is the approximate mass per cent of \(\mathrm{Mn}\) in it? \((\mathrm{Mn}=55)\) (a) \(66.67\) (b) \(24.02\) (c) \(72.05\) (d) \(69.62\)

Short answer

69.62

Step-by-step solution

Convert mol percent to mass percent for MnO

For MnO, we calculate the mass percent of Mn present by multiplying the atomic mass of Mn (55) with the mol percent of MnO (66.67) and dividing by the molar mass of MnO (55 + 16 = 71). This gives us the mass of Mn contributed by MnO.

Convert mol percent to mass percent for MnO2

For MnO2, we calculate the mass percent of Mn present by taking the remaining mol percent (100 - 66.67) for MnO2, calculating the mass of Mn as if all were MnO2, then dividing by the combined molar mass of MnO and MnO2 with their respective mol percentages.

Calculate the total mass percent of Mn

We add the contributions from both MnO and MnO2 to get the total mass percent of Mn in the mixture.

Key concepts

Mol Percent to Mass Percent Conversion

Understanding the conversion of mol percent to mass percent is essential for analyzing the composition of chemical mixtures. Mol percent, or mole fraction, is a way of expressing the concentration of a component in a mixture by comparing the number of moles of the component to the total number of moles of all components. However, when we seek to understand the actual mass contribution of each component, we must convert this ratio into mass percent.

The procedure begins with knowing the mol percent and the atomic or molecular mass of the component in question. To convert, multiply the atomic or molecular mass of the component with its mol percent and then divide by the molar mass of the whole substance or mixture. This gives you the mass percent contribution of that specific component. Specifically for metals, such as manganese (Mn) in our exercise, this conversion elucidates what portion of the mixture’s total mass is due to Mn atoms, irrespective of the specific manganese compound they are part of.

Molar Mass Calculation

Molar mass is a critical factor in the conversion between moles and grams, which are standard units in chemical calculations. The molar mass is defined as the mass of one mole of a given substance (elements or compounds) and is typically expressed in grams per mole (g/mol). For an element, the molar mass is equal to the atomic mass found on the periodic table, as in the case of manganese (Mn) which has a molar mass of approximately 55 g/mol.

When dealing with compounds like MnO or MnO2, the molar mass is the sum of the atomic masses of all the atoms present in the compound’s chemical formula. For instance, MnO has a molar mass of 71 g/mol (55 g/mol for Mn + 16 g/mol for O), while MnO2 has a molar mass of 87 g/mol (55 g/mol for Mn + 2 × 16 g/mol for O). Accurate calculation of molar masses allows for precise stoichiometric conversions and is crucial when determining mass percent compositions in mixtures.

Chemical Compound Mixture

A chemical compound mixture, such as a combination of MnO and MnO2, consists of two or more substances mixed together without any chemical bonding between them. Each substance retains its own chemical identity and properties within the mixture. In such mixtures, the concentration of each component can vary, unlike in pure compounds where the composition is constant.

An understanding of the relationship between the components in a mixture is vital when it comes to manipulating and predicting the properties and reactions of the mixture. The mass percent composition indicates how much of each compound is present in terms of mass, providing insight into the mixture’s overall makeup. In our MnO and MnO2 example, the mass percent of Mn in the mixture can tell us how manganese-rich the material is, which is particularly important in industrial applications where specific properties are desired.