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Chapter 1: Problem 14

A sodium chloride solution was prepared in the following manner: \- A \(25.0 \mathrm{~mL}\) volumetric flask (Figure \(1.8)\) was placed on an analytical balance and found to have a mass of \(35.6783 \mathrm{~g}\). \- Sodium chloride was added to flask and the mass of the solid \(+\) flask was \(36.2365 \mathrm{~g}\). \- The flask was filled to the mark with water and mixed well. Calculate the concentration of the sodium chloride solution in units of \(\mathrm{g} / \mathrm{mL}\) and give the answer in scientific notation with the correct number of significant figures.

Short Answer

Expert verified
The concentration of the sodium chloride solution is approximately \(2.233 \times 10^{-2}\) g/mL.

Step by step solution

01

Determine the Mass of Sodium Chloride

First, find the mass of sodium chloride by subtracting the mass of the empty flask from the mass of the flask with the sodium chloride. The mass of the sodium chloride is calculated as follows: \[ \text{Mass of NaCl} = \text{Mass of flask + NaCl} - \text{Mass of flask} = 36.2365 \text{ g} - 35.6783 \text{ g} = 0.5582 \text{ g} \]
02

Use the Flask Volume for Concentration

The concentration of the solution is calculated by dividing the mass of sodium chloride by the volume of the solution, which is the volume of the flask: \[ \text{Volume of solution} = 25.0 \text{ mL} \]
03

Calculate Concentration in g/mL

Using the mass of the sodium chloride and the volume of the solution, calculate the concentration: \[ \text{Concentration} = \frac{\text{Mass of NaCl}}{\text{Volume of solution}} = \frac{0.5582 \text{ g}}{25.0 \text{ mL}} \approx 0.022328 \text{ g/mL} \]
04

Express the Concentration in Scientific Notation

Convert the concentration into scientific notation with the correct number of significant figures. Since the original mass of sodium chloride has four significant figures, the concentration should also have four significant figures: \[ 0.022328 \text{ g/mL} \approx 2.233 \times 10^{-2} \text{ g/mL} \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Volumetric Flask Usage
When measuring substances for a chemical solution, using a volumetric flask is crucial due to its precision. A volumetric flask is specifically designed for measuring accurate liquid volumes. It has a narrow neck with a single calibration mark to ensure accurate measurement when preparing solutions.

To use the volumetric flask effectively, follow these steps:
  • Ensure the flask is clean and dry before use. Residues can affect the solution's concentration.
  • Weigh the flask while it鈥檚 empty to establish a baseline mass.
  • After adding the desired chemical (like sodium chloride in our example), re-weigh the flask to determine the exact mass of the chemical alone.
  • Fill the flask with solvent (usually water) up to the etched "fill line" on the neck. This ensures that the volume is precise to the specified capacity, in this case, 25.0 mL.
  • Mix the solution thoroughly for an even concentration throughout the liquid.
The accuracy of volumetric flasks makes them essential in preparing solutions with precise molarity.
Significant Figures in Calculations
In any scientific measurement, significant figures help communicate the precision of your results. When working with chemical solutions, keeping track of significant figures is vital to avoid reporting misleading precision.

Here are some guidelines for significant figures:
  • Non-zero digits are always significant. For example, in 36.2365 g, all numbers are significant.
  • Any zeros between significant digits are also significant. For instance, in 25.0 mL, all three digits count as significant because the zero is trailing a decimal.
  • In scientific notation, only the digits in the coefficient are considered for significant figures. So, in 2.233 脳 10-2 g/mL, there are four significant figures.
  • Your final answer should reflect the precision of the initial data, rounding to the lowest number of significant figures from your measurements.
In the exercise, the flask's measurements had up to four significant figures, so the resulting concentration in scientific notation also used four.
Scientific Notation in Chemistry
Scientific notation is a technique used to express very large or very small numbers succinctly and makes calculation simpler. In chemistry, it helps in presenting concentrations and other measurements in a format that's easy to read and understand.

The steps to correctly use scientific notation in chemistry are:
  • Identify the significant figures in the number you need to express. In our example, the concentration was initially 0.022328 g/mL.
  • Move the decimal point to get a number between 1 and 10. For 0.022328, it becomes 2.233 by moving the decimal two places to the right.
  • Multiply this number by 10 raised to the power of how many places you moved the decimal. Here, it's 2.233 脳 10-2.
  • Ensure the correct significant figures are reflected, typically mirroring as many as the least precise measurement in your calculation.
Scientific notation simplifies complex calculations and ensures results are communicated clearly and precisely, which is essential in scientific communication.

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Most popular questions from this chapter

Platinum is an expensive and rare metal used in catalytic converters and other industrial applications. Much research has been devoted to maximizing reactive properties of other metals by shrinking them to nanoparticles in the hope that someday they will be an efficient and economic alternative to platinum. (a) Explain why changing the size of a metal particle influences its reactivity. (b) What is the economic benefit of using small particles? (c) What properties other than reactivity might you expect to change as the size of particle approaches the nanoscale?

Ocean currents are measured in Sverdrups \((\mathrm{sv})\) where \(1 \mathrm{sv}=10^{9} \mathrm{~m}^{3} / \mathrm{s}\). The Gulf Stream off the tip of Florida, for instance, has a flow of \(35 \mathrm{sv}\) (a) What is the flow of the Gulf Stream in milliliters per minute? (b) What mass of water in the Gulf Stream flows past a given point in 24 hours? The density of seawater is \(1.025 \mathrm{~g} / \mathrm{mL}\). (c) How much time is required for 1 petaliter \(\left(\mathrm{PL} ; 1 \mathrm{PL}=10^{15} \mathrm{~L}\right)\) of seawater to flow past a given point?

What is the density of lead in \(\mathrm{g} / \mathrm{cm}^{3}\) if a rectangular bar measuring \(0.50 \mathrm{~cm}\) in height, \(1.55 \mathrm{~cm}\) in width, and \(25.00 \mathrm{~cm}\) in length has a mass of \(220.9 \mathrm{~g}\) ?

Convert the following quantities into SI units with the correct number of significant figures: (a) \(5.4\) in. (b) \(66.31 \mathrm{lb}\) (c) \(0.5521\) gal (d) \(65 \mathrm{mi} / \mathrm{h}\) (e) \(978.3 \mathrm{yd}^{3}\) (f) \(2.380 \mathrm{mi}^{2}\)

Administration of digitalis, a drug used to control atrial fibrillation in heart patients, must be carefully controlled because even a modest overdose can be fatal. To take differences between patients into account, drug dosages are prescribed in terms of \(\mathrm{mg} / \mathrm{kg}\) body weight. Thus, a child and an adult differ greatly in weight, but both receive the same dosage per kilogram of body weight. At a dosage of \(20 \mu \mathrm{g} / \mathrm{kg}\) body weight, how many milligrams of digitalis should a \(160 \mathrm{lb}\) patient receive?
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