Chapter 13: Problem 47
Ocean water contains \(3.5 \% \mathrm{NaCl}\) by mass. How much salt can be obtained from \(254 \mathrm{~g}\) of seawater?
Short Answer
Expert verified
8.89 grams of NaCl can be obtained from 254 grams of seawater.
Step by step solution
01
Understanding the Percentage by Mass
Ocean water contains 3.5% NaCl by mass, which means that for every 100 grams of seawater, there are 3.5 grams of NaCl. To find the amount of NaCl in 254 grams of seawater, you need to calculate 3.5% of 254 grams.
02
Calculating the Mass of NaCl
To find the mass of NaCl in 254 grams of seawater, the percentage needs to be converted to a decimal by dividing it by 100 and then multiplied by the mass of the seawater. This can be expressed as: Mass of NaCl = (Percentage of NaCl in decimal form) x (Mass of seawater).Substitute the known values to get: Mass of NaCl = \(0.035 \times 254 \mathrm{g}\).
03
Performing the Calculation
Perform the calculation from the previous step:Mass of NaCl = \(0.035 \times 254 \mathrm{g}\) = 8.89 grams. The mass of NaCl obtained from 254 grams of seawater is 8.89 grams (after rounding to two decimal places).
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Mass Percentage Calculation
When dealing with chemical solutions, the mass percentage is a crucial concept used to express the concentration of a component in a mixture. It is defined as the mass of the solute (the dissolved substance) divided by the total mass of the solution (the mixture of solute and solvent), and multiplied by 100%. Understanding this concept helps in precisely describing the composition of mixtures in chemistry.
In practical terms, if ocean water contains 3.5% NaCl by mass, this indicates there are 3.5 grams of sodium chloride (NaCl) in every 100 grams of seawater. When trying to determine the amount of NaCl in a different quantity of seawater, we apply a simple formula: \[ \text{Mass of NaCl} = \left( \frac{\text{Percentage of NaCl}}{100} \right) \times \text{Mass of seawater} \].
For a given sample, the mass percentage allows us to calculate the exact amount of a substance contained in the mixture. It's important to convert the percentage to a decimal before multiplying by the mass, which is a common mistake to avoid.
In practical terms, if ocean water contains 3.5% NaCl by mass, this indicates there are 3.5 grams of sodium chloride (NaCl) in every 100 grams of seawater. When trying to determine the amount of NaCl in a different quantity of seawater, we apply a simple formula: \[ \text{Mass of NaCl} = \left( \frac{\text{Percentage of NaCl}}{100} \right) \times \text{Mass of seawater} \].
For a given sample, the mass percentage allows us to calculate the exact amount of a substance contained in the mixture. It's important to convert the percentage to a decimal before multiplying by the mass, which is a common mistake to avoid.
Stoichiometry
Stoichiometry is the section of chemistry that deals with the quantitative relationships between the substances involved in chemical reactions. It is based on the law of conservation of mass and the concept of the mole, which is a count of a number of particles, such as atoms, molecules, or ions in a sample.
Stoichiometry involves using balanced chemical equations to determine the proportions of reactants and products. It's essential for predicting yields, optimizing reactions, and scaling up from laboratory to production. For example, if we wanted to neutralize a certain amount of hydrochloric acid (HCl) with sodium hydroxide (NaOH), we'd need to use stoichiometry to calculate the precise amount of NaOH required for complete neutralization.
The stoichiometric calculations can extend beyond reacting particles to include mass, volume, and concentration, allowing us to solve problems like determining the amount of salt in seawater. Applying stoichiometry to our seawater example, we considered only the direct relationship between mass of seawater and mass of NaCl, which simplifies the problem, as no chemical reaction was involved.
Stoichiometry involves using balanced chemical equations to determine the proportions of reactants and products. It's essential for predicting yields, optimizing reactions, and scaling up from laboratory to production. For example, if we wanted to neutralize a certain amount of hydrochloric acid (HCl) with sodium hydroxide (NaOH), we'd need to use stoichiometry to calculate the precise amount of NaOH required for complete neutralization.
The stoichiometric calculations can extend beyond reacting particles to include mass, volume, and concentration, allowing us to solve problems like determining the amount of salt in seawater. Applying stoichiometry to our seawater example, we considered only the direct relationship between mass of seawater and mass of NaCl, which simplifies the problem, as no chemical reaction was involved.
Solution Concentration
Solution concentration describes how much solute is dissolved in a specific amount of solvent. In chemistry, there are several ways to express concentration, including molarity, molality, and mass percentage. The mass percentage, also known as weight/weight percentage, is one of the simplest forms of expressing concentration, especially when dealing with solid solutes and liquid solvents.
The concentration of a solution can significantly affect the properties and behavior of the solution, such as boiling point, freezing point, and reactivity. Thus, understanding how to calculate and interpret solution concentration is essential in various fields such as pharmacy, environmental science, and chemical engineering. For example, when we say ocean water has 3.5% NaCl by mass, we communicate a specific concentration that defines the ocean's 'salinity', which in turn influences marine life and ecosystems.
When calculating the concentration of a solution or the mass of solute that can be obtained from a solution, it's important to be familiar with the unit being used; in our case, the mass percentage serves as a straightforward dimension to approach the problem—highlighting just one of the versatile methods chemists have at their disposal for comparing solution concentrations.
The concentration of a solution can significantly affect the properties and behavior of the solution, such as boiling point, freezing point, and reactivity. Thus, understanding how to calculate and interpret solution concentration is essential in various fields such as pharmacy, environmental science, and chemical engineering. For example, when we say ocean water has 3.5% NaCl by mass, we communicate a specific concentration that defines the ocean's 'salinity', which in turn influences marine life and ecosystems.
When calculating the concentration of a solution or the mass of solute that can be obtained from a solution, it's important to be familiar with the unit being used; in our case, the mass percentage serves as a straightforward dimension to approach the problem—highlighting just one of the versatile methods chemists have at their disposal for comparing solution concentrations.