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Chapter 1: Problem 17

Any dilute aqueous solution has a density near \(1.00 \mathrm{~g} / \mathrm{mL}\). Suppose the solution contains \(1 \mathrm{ppm}\) of solute; express the concentration of solute in \(\mathrm{g} / \mathrm{L}, \mu \mathrm{g} / \mathrm{L}, \mu \mathrm{g} / \mathrm{mL}\), and \(\mathrm{mg} / \mathrm{L}\).

Short Answer

Expert verified
The concentration is 0.001 g/L, 1000 渭g/L, 1 渭驳/尘尝, and 1 mg/L.

Step by step solution

01

Understand the meaning of 1 ppm

A concentration of 1 ppm (part per million) means 1 gram of solute per 1 million grams of solution. Since the density of the solution is approximately 1 g/mL, 1 million grams of solution is equivalent to 1 million milliliters, or 1000 liters.
02

Convert ppm to g/L

Since 1 ppm is equivalent to 1 gram of solute in 1000 L of solution, it translates directly to 1 g/1000 L. Therefore, the concentration is \( \frac{1}{1000} \) g/L, which simplifies to 0.001 g/L.
03

Convert g/L to 渭g/L

To convert grams to micrograms, multiply by 1,000,000 (since there are 1,000,000 micrograms in a gram). Thus, the concentration of 0.001 g/L becomes \( 0.001 \times 1,000,000 = 1000 \) 渭g/L.
04

Convert g/L to 渭驳/尘尝

Since 1 渭g/L is equal to 0.001 渭驳/尘尝 (because there are 1,000 mL in a liter), you can convert 1000 渭g/L to 渭驳/尘尝 by dividing by 1000: \( \frac{1000}{1000} = 1 \) 渭驳/尘尝.
05

Convert g/L to mg/L

To convert grams to milligrams, multiply by 1,000 (since there are 1,000 milligrams in a gram). Thus, the concentration of 0.001 g/L becomes \( 0.001 \times 1,000 = 1 \) mg/L.

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Key Concepts

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

ppm
When people talk about parts per million, or ppm, they're discussing a way to express concentrations. It helps in understanding the amount of a substance present in a particular mixture, even if it's very tiny. In simpler terms, 1 ppm is like having 1 part of a solute, or minor component, in a million parts of the total solution.
Imagine having a mixture with a total mass of 1,000,000 grams (or 1 million grams) and spotting just 1 gram of a special ingredient within it鈥攖hat's 1 ppm.
  • This measurement is especially useful in water quality checks, air quality assessments, and even in food safety, where minute concentrations need to be monitored.
  • Understanding ppm helps you calculate other units of concentration easily, like converting to grams per liter.
g/L
Grams per liter (g/L) is a direct way to convey concentration levels in liquids, especially for solutions like those in chemistry labs. It acts as a straightforward depiction of how many grams of a solute are found in one liter of solution.
With 1 ppm equivalent to 0.001 g/L, realizing that there's 0.001 grams of solute in every liter of solution becomes simple.
  • Since g/L gives you a more grounded sense of the weight of a substance in a given volume, many scientists find it practical for calculations and predictions.
  • It's crucial in fields like pharmacology and engineering, where precise calculations are significant.
mg/L
Milligrams per liter (mg/L) is akin to g/L but focuses on smaller amounts since it breaks grams into milligrams. It reflects how many milligrams of a substance are present in each liter of a solution.
For converting from g/L, simply multiply by 1,000 (because 1 gram equals 1,000 milligrams). Thus, 0.001 g/L is equivalent to 1 mg/L.
  • This unit is prevalent in environmental science, especially in water testing, as it commonly represents concentrations like those of dissolved oxygen or contaminants.
  • It鈥檚 often a favored unit due to its balance between precision and simplicity for conveying low but important concentrations.
渭驳/尘尝
Micrograms per milliliter (渭驳/尘尝) is a concentration metric that offers a focused glimpse into how much of a solute exists in a tiny volume, making it invaluable in scenarios needing high precision, like medical dosing.
To derive 渭驳/尘尝 from 渭g/L, remember that 1,000 liters hold 1,000,000 milliliters, so dividing by 1,000 gives you this concentration. For example, 1,000 渭g/L turns into 1 渭驳/尘尝.
  • This unit is commonly applied in pharmaceuticals, nutrient concentrations, and even in laboratory tests.
  • Understanding 渭驳/尘尝 is key when you require precision, especially in health sectors, where dosage accuracy can have sweeping impacts.

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Most popular questions from this chapter

Sulfamic acid is a primary standard that can be used to standardize \(\mathrm{NaOH}\). $$ { }^{+} \mathrm{H}_{3} \mathrm{NSO}_{3}^{-}+\mathrm{OH}^{-} \quad \longrightarrow \quad \mathrm{H}_{2} \mathrm{NSO}_{3}^{-}+\mathrm{H}_{2} \mathrm{O} $$ Sulfamic acid FM \(97.094\) What is the molarity of a sodium hydroxide solution if \(34.26 \mathrm{~mL}\) react with \(0.3337 \mathrm{~g}\) of sulfamic acid?

What is the formal concentration (expressed as \(\mathrm{mol} / \mathrm{L}=\mathrm{M}\) ) of \(\mathrm{NaCl}\) when \(32.0 \mathrm{~g}\) are dissolved in water and diluted to \(0.500 \mathrm{~L}\) ?

A cell in your adrenal gland has about \(2.5 \times 10^{4}\) tiny compartments called vesicles that contain the hormone epinephrine (also called adrenaline). (a) An entire cell has about \(150 \mathrm{fmol}\) of epinephrine. How many attomoles (amol) of epinephrine are in each vesicle? (b) How many molecules of epinephrine are in each vesicle? (c) The volume of a sphere of radius \(r\) is \(\frac{4}{3} \pi r^{3}\). Find the volume of a spherical vesicle of radius \(200 \mathrm{~nm}\). Express your answer in cubic meters \(\left(\mathrm{m}^{3}\right)\) and liters, remembering that \(1 \mathrm{~L}=10^{-3} \mathrm{~m}^{3}\). (d) Find the molar concentration of epinephrine in the vesicle if it contains 10 amol of epinephrine.

How many milliliters of \(3.00 \mathrm{M} \mathrm{H}_{2} \mathrm{SO}_{4}\) are required to react with \(4.35 \mathrm{~g}\) of solid containing \(23.2 \mathrm{wt} \% \mathrm{Ba}\left(\mathrm{NO}_{3}\right)_{2}\) if the reaction is \(\mathrm{Ba}^{2+}+\mathrm{SO}_{4}^{2} \rightarrow \mathrm{BaSO}_{4}(s) ?\)

How many joules per second \((\mathrm{J} / \mathrm{s})\) are used by a device that requires \(5.00 \times 10^{3}\) British thermal units per hour \((\mathrm{Btu} / \mathrm{h})\) ? How many watts (W) does this device use?
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