Chapter 11: Problem 31
What are the mole fractions of \(\mathrm{HNO}_{3}\) and water in a concentrated solution of nitric acid \(\left(68.0 \% \mathrm{HNO}_{3} \mathrm{by}\right.\) mass)? (a) Outline the steps necessary to answer the question. (b) Answer the question.
Short Answer
Expert verified
The mole fraction of \(\mathrm{HNO}_{3}\) is approximately 0.796 and the mole fraction of water is approximately 0.204.
Step by step solution
01
Identify Required Quantities
To solve for the mole fractions of \(\mathrm{HNO}_{3}\) and water in the solution, first determine the mass of each component in a given total mass of the solution. Assume a total solution mass of 100 g to simplify calculations using the percentage given.
02
Calculate Mass of Each Component
Calculate the mass of \(\mathrm{HNO}_{3}\) by taking 68.0% of the total solution mass. Calculate the mass of water by subtracting the mass of \(\mathrm{HNO}_{3}\) from the total mass.
03
Convert Mass to Moles
Convert the mass of \(\mathrm{HNO}_{3}\) and water to moles. Use the molar masses of \(\mathrm{HNO}_{3}\) (63.01 g/mol) and water (18.02 g/mol).
04
Calculate Mole Fractions
The mole fraction is calculated by dividing the moles of each component by the total moles in the solution. So, find the mole fraction for \(\mathrm{HNO}_{3}\) and for water by dividing their respective mole amounts by the sum of both.
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Concentration Solution Calculation
When tasked with determining the concentration of a solution, one often refers to the term 'mole fraction'. The mole fraction represents the proportion of a constituent to the total amount of all constituents in the mixture, expressed in moles. To calculate the mole fraction, one must know the moles of each substance present in the solution.
For example, in a concentrated nitric acid solution (HNO3) with a certain percentage by mass, the mole fraction of HNO3 and water (H2O) can be found following these steps:
As learning becomes more effective with practice, seeking exercises that involve a range of concentrations can help solidify your understanding of solution concentration calculations.
For example, in a concentrated nitric acid solution (HNO3) with a certain percentage by mass, the mole fraction of HNO3 and water (H2O) can be found following these steps:
- First, assume a convenient total mass for the solution, such as 100 grams to make use of the given percentage directly.
- Calculate the mass of HNO3 by applying the percentage to the total mass.
- Then, subtract this value from the total mass to find the mass of water.
- Convert the mass of each component to moles using their respective molar masses.
- Finally, divide the moles of each substance by the total moles to obtain their mole fractions.
As learning becomes more effective with practice, seeking exercises that involve a range of concentrations can help solidify your understanding of solution concentration calculations.
Mass to Mole Conversion
Mass to mole conversion is an essential step in chemistry calculations and requires the application of the molar mass of a substance. This process transforms the mass of a substance into the amount in moles, which is a fundamental concept for understanding chemical quantities.
The conversion involves the following:
For instance, if you have 68 grams of HNO3 with a molar mass of 63.01 g/mol, the number of moles can be calculated by dividing the mass by the molar mass, that is, 68 g / 63.01 g/mol. Implementing such calculations with different compounds reinforces your ability to interconvert mass and moles efficiently.
The conversion involves the following:
- Identify the molar mass of the substance, which is the mass per mole of its particles, typically found in grams per mole (g/mol).
- Use the molar mass as a conversion factor where the molar mass expressed in grams corresponds to one mole of the substance.
For instance, if you have 68 grams of HNO3 with a molar mass of 63.01 g/mol, the number of moles can be calculated by dividing the mass by the molar mass, that is, 68 g / 63.01 g/mol. Implementing such calculations with different compounds reinforces your ability to interconvert mass and moles efficiently.
Molar Mass
Molar mass is a critical property of substances that links the mass of a sample to the amount of substance in moles. It is the mass of one mole of particles (atoms, molecules, or ions) and is expressed in units of grams per mole (g/mol).
Here are key points regarding molar mass:
Knowing the molar mass is indispensable for converting between mass and moles. For example, HNO3 has a molar mass of 63.01 g/mol, which means 63.01 grams of HNO3 constitutes one mole. Accurate molar mass values ensure reliable stoichiometric calculations and are fundamental in understanding the composition of compounds.
Here are key points regarding molar mass:
- The molar mass can be calculated by summing the atomic masses of all the atoms in a molecule.
- The atomic masses are obtained from the periodic table and typically represent the average mass of all isotopes of an element as they occur in nature.
Knowing the molar mass is indispensable for converting between mass and moles. For example, HNO3 has a molar mass of 63.01 g/mol, which means 63.01 grams of HNO3 constitutes one mole. Accurate molar mass values ensure reliable stoichiometric calculations and are fundamental in understanding the composition of compounds.
Percentage Composition
Percentage composition refers to the percentage by mass of each element within a compound. This is a vital concept for understanding the make-up of compounds and for performing various chemical calculations.
Here's a brief overview:
When working with solutions, like a 68% HNO3 solution, the percentage composition tells us that 68 grams of HNO3 are present in every 100 grams of solution. Grasping this concept is essential for preparatory steps in many stoichiometric and analytical calculations, and it lays the groundwork for more advanced topics in chemistry. Regularly practicing calculations involving percentage composition can aid in building a strong foundation in chemical analysis.
Here's a brief overview:
- Calculate the mass of each element in a compound and divide it by the molar mass of the entire compound.
- Multiply the resulting fraction by 100 to convert it to a percentage.
When working with solutions, like a 68% HNO3 solution, the percentage composition tells us that 68 grams of HNO3 are present in every 100 grams of solution. Grasping this concept is essential for preparatory steps in many stoichiometric and analytical calculations, and it lays the groundwork for more advanced topics in chemistry. Regularly practicing calculations involving percentage composition can aid in building a strong foundation in chemical analysis.