Tag Archives: units

How Much Does a Gallon of Water Weigh? Easy Calculation

Question: How much does a gallon of water weigh?

Ever wonder how much a gallon of water weighs? A US gallon is 8.34 lbs or 3.78 kg. (David Mulder)

Ever wonder how much a gallon of water weighs? A US gallon is 8.34 lbs or 3.78 kg. (David Mulder)

Answer: A US gallon of water weighs 8.34 lbs or 3.78 kg at 62 °F (17 °C). An imperial gallon (UK) weighs 10.022 lbs or 4.546 kg, at its most dense temperature, which is 2.20456 lbs / L at 4 °C or 39 °F.

Ballpark Calculation (for all temperatures)

1 gallon is about 3.75 liters
1 liters = 1 kilogram (density of water is 1 kg/liter)
1 kg is about 2.2 lbs
so, 3.75 kg is about 8.25 lbs and 1 gallon is about 8.25 lbs

Three Different Units of Gallon

It makes a difference which unit of gallon you are using. There are two US definitions of gallon. The US liquid gallon (most commonly used) is defined as 231 cubic inches, which is 3.785 liters, and weighs 8.344 lbs at its highest density.

The US dry gallon is defined as 1/8th of a US bushel, which is 268.8025 cubic inches or 4.405 L. The weight of a US dry gallon is 9.711 lbs of water at its highest density.

The UK gallon or imperial gallon originally was defined as 10 lbs of water, but the modern definition is exactly 4.54609 L or 10.02 lbs of water at its maximum density.

Effect of Water Temperature on Weight

Cold water is more dense than ice or than warm water or liquid just above freezing. This is an unusual property of the substance, resulting from hydrogen bonding. So, a gallon of warm water would weigh slightly less than a gallon of cold water. The exact difference would depend on the temperatures in question, but it doesn’t affect the value by much.

Of course, gravity affects weight too, so a gallon of water (or anything else) would weigh more on Jupiter than on Earth, while it would weigh less on the Moon than Earth.

Easy Way To Remember the Weight of Water

While you’ll want to keep the exact volume definitions in mind for scientific calculations, for everyday use you can remember the weight of water using the simple rhyme: A pint’s a pound, the world round.

The saying refers to the rough equivalence between 16 fluid ounces (a pint) and 16 ounces avoirdupois weight. A gallon is 4 quarts or 8 points, so a gallon weighs approximately 8 lbs.

Karat vs Carat – Understand the Difference Between Karats and Carats

What’s the difference between karats and carats? Are they the same?

Carat vs Karat: A carat is a unit of gemstone mass equal to 200 mg, while a karat is a measure of gold purity. (photos: Mario Sarto, Agnico-Eagle)

Carat vs Karat: A carat is a unit of gemstone mass equal to 200 mg, while a karat is a measure of gold purity. (photos: Mario Sarto, Agnico-Eagle)

The terms karats and carats are both used to refer to bling in the jewelry trade and in geology, but the words don’t mean the same thing.

A carat is a unit of mass used in the jewelry industry to describe the weight of diamonds and other gemstones. One carat is equal to 200 milligrams or 0.2 grams. To put this into perspective, a pound is 453 grams or 2264 carats. A 2-carat diamond would weigh 400 mg. Gemstones have different densities, so 1 carat of one stone might be larger or smaller in volume than 1 carat of another material. A carat may be divided into 100 points, each with a mass of 2 milligrams. The abbreviation for carats is CT or ct.

A karat is a term used to describe the purity of gold. A karat is 1/24th of a portion, so 24 karat gold is pure gold. 14-karat gold is 14 parts gold and 10 parts other metals. 18-karat gold is 18/24 parts gold or 75% gold. Pure gold is very soft, so it’s usually mixed with other metals to form an alloy that’s hard, less expensive, and sometimes has a different color. The abbreviation for karat is K or k, as in “14k gold”.

History of the Terms Carat and Karat

The word carat comes from a Greek word, meaning “carob seed”. The seeds were units of weight for small objects, as measured on balances. The carat came into use for measuring the weight of diamonds in the 1570s. While some people surmised carob seeds were used because they were uniform in weight, this isn’t actually true. The size and mass of these seeds varies about as much as for other species. Until 1907, the mass of a carat varied from one country to another, ranging from 187 mg in Cyprus to 216 mg in Livorno. The unit was standardized to become the 200 mg metric carat, which is the unit used today throughout the world.

“Karat” is a variant of the word “carat”. There is no recorded mention of carob seeds ever being used to measure gold. At some point, the gemstone mass term and gold purity term diverged. In 309 CE, the Roman emperor Constantine I minted gold coins that were the mass of 24 siliqua, where a siliqua or carat was 1/1728 of a libra or pound. This is probably the origin of the use of 24 parts for karats. The term karat is only used to describe purity or fineness of gold. It is 24 times the pure mass divided by the total mass:

K = 24 x (Mg/Mm)

where K is the karat rating, Mg is mass of gold, and Mm is total mass.

Did You Know?

  • A “paragon” is a flawless diamond weighing at least 100 carats.
  • The ANSI X.12 EDI standard abbreviation for the unit carat is CD.
  • Millesimal fineness is another unit used to measure purity of gold. The term is also applied to other precious metals, such as silver and platinum. The term refers to parts per thousands, so 18k gold, which is 75% gold or 750 parts per 1000 would be called “750”. Usually, millesimal fineness is rounded to three figures, but it can be used to describe high purity. For example, extremely pure gold that is 99.99% pure, is called “9999” or “four nines fine”. The finest gold ever produced was six nines fine (refined by the Perth Mint in 1957).

 

Physical Constants, Prefixes, and Conversion Factors

Here are some useful physical constants, conversion factors, and unit prefixes. They are used in many calculations in chemistry, as well as in physics and other sciences.

Useful Constants

Acceleration of Gravity9.806 m/s2
Avogadro’s Number6.022 x 1023
Electronic Charge1.602 x 10-19 C
Faraday Constant9.6485 x 104 J/V
Gas Constant0.08206 L·atm/(mol·K)

8.314 J/(mol·K)

8.314 x 107 g·cm2/(s2·mol·K)

Planck’s Constant6.626 x 10-34 J·s
Speed of Light2.998 x 108 m/s
p3.14159
e2.718
ln x2.3026 log x
2.3026 R19.14 J/(mol·K)
2.3026 RT (at 25°C)5.708 kJ/mol

Common Conversion Factors

QuantitySI UnitOther UnitConversion Factor
Energyjoulecalorie
erg
1 cal = 4.184 J
1 erg = 10-7 J
Forcenewtondyne1 dyn = 10-5 N
LengthmetreAngstrom1 Å = 10-10 m = 10-8 cm = 10-1 nm
Masskilogrampound1 lb = 0.453592 kg
Pressurepascalbar
atmosphere
mm Hg
lb/in2
1 bar = 105 Pa
1 atm = 1.01325 x 105 Pa
1 mm Hg = 133.322 Pa
1 lb/in2 = 6894.8 Pa
TemperaturekelvinCelsius
Fahrenheit
1°C = 1 K
1°F = 5/9 K
Volumecubic metrelitre
gallon (U.S.)
gallon (U.K.)
cubic inch
1 L = 1 dm3 = 10-3 m3
1 gal (U.S.) = 3.7854 x 10-3 m3
1 gal (U.K.) = 4.5641 x 10-3 m3
1 in3 = 1.6387 x 10-6 m3

SI Unit Prefixes

FactorsPrefixSymbol
1012teraT
199gigaG
106megaM
103kilok
102hectoh
101decada
10-1decid
10-2centic
10-3millim
10-6microµ
10-9nanon
10-12picop
10-15femtof
10-18attoa

 

Concentration Units For Solutions

Beaker and FlaskChemistry is a science which deals a lot with solutions and mixtures. Knowing just how much of one thing is mixed in with a solution is an important thing to know. Chemists measure this by determining the concentration of the solution or mixture.

There are three terms that need to be defined in concentration discussions: solute, solvent and solution.

Solute: The dissolved substance added to the solution.
Solvent: The liquid that dissolves the solute.
Solution: The combination of solute and solvent.

The relationship between these three terms is expressed by many different concentration units. The unit you choose to use depends on how the solution is going to be used in your experiments. Common units include molarity, molality, and normality. Others are mass percent, mole fraction, formality and volume percent. Each unit is explained along with information about when to use them and the formulas needed to calculate the unit.

Molarity

Molarity is the most common concentration unit. It is a measure of the number of moles of solute in one liter of solution. Molarity measurements are denoted by the capital letter M with units of moles/Liter.

The formula for molarity (M) is

This shows the number of moles of solute dissolved in a liquid to make one liter of solution. Note the amount of solvent is unknown, just that you end up with a known volume of solution.

A 1 M solution will have one mole of solute per liter of solution.  100 mL will have 0.1 moles, 2L will have 2 moles, etc.

Molarity Example Problem

Molality

Molality is another commonly used concentration unit. Unlike molarity, molality is interested in the solvent used to make the solution.

Molality is a measure of the number of moles of solute dissolved per kilogram of solvent. This unit is denoted by the lower case letter m.

The formula for molality (m) is

molality formula

Molality is used when temperature is part of the reaction. The volume of a solution can change when temperature changes. These changes can be ignored if the concentration is based on mass of the solvent.

Molality Example Problem

Normality

Normality is a concentration unit seen more often in acid-base and electrochemistry solutions. It is denoted by the capital letter L with units of moles/L. Normality is more concerned with the chemically active part of the solution. For example, take two acid solutions, hydrochloric (HCl) acid and sulfuric (H2SO4) acid. A 1 M solution of HCl contains one mole of H+ ions and one mole of Cl ions where a 1 M solution of H2SO4 contains 2 moles of H+ ions and one mole of SO4 ions. The sulfuric acid produces twice the number of active H+ ions as the same concentration of HCl. Normality addresses this with the idea of chemical equivalent units. Equivalent units are the ratio of the number of moles of solute to the number of moles needed to produce 1 mole of the active ion. In our example, this ratio is 1:1 for HCl, both H+ and Cl ions so the equivalent unit for both ions is 1. For H2SO4, the ratio is 1:12 for H+ and 1:1 for SO4. The equivalent unit for H+ is 2 and 1 for SO4.

This number is used to calculate the normality of a solution using the formula

Note it is essentially the same as the molarity equation with the addition of equivalent units.
For our example, the 1 M solution of HCl would have a normality of 1 N for both H+ and Cl and the 1 M H2SO4 would have a normality of 2 N for H+ and 1 N for SO4.

Mass Percent, Parts per Million and Parts per Billion

Mass percent or mass percent composition is a measurement to show the percentage composition by mass of one part of a solution or mixture. It is most often represented by a % symbol.

The formula for mass percent is

where A is the part needed and the total is the total mass of the solution or mixture. If all the mass percent parts are added together, you should get 100%.

Mass Percent Example

If you think of mass percent as parts per hundred, you can make the leap to the units of parts per million (ppm) and parts per billion (ppb). These two units are used when the solute’s concentration is very small compared to the volume measured.

The formula for parts per million is

and parts per billion

Note the similarity between mass% and these two equations.

Volume Percent

Volume percent is a concentration unit used when mixing two liquids. When pouring two different liquids together, the new combined volume may not be equal to the sum of their initial volumes. Volume percent is used to show the ratio of the solute liquid to the total volume.

The formula is very similar to the mass percent, but uses volume in place of the mass. VolumeA is the volume of the solute liquid and the volumeTOTAL is the total volume of the mixture.

On a side note, v/v % measurements of alcohol and water are labelled commercially with the unit known as Proof. Proof is twice the v/v % measurement of ethanol in the beverage.

Mole Fraction

Mole fraction is the ratio of the number of moles of a single component of a solution to the total number of moles present in the solution.

Mole fractions are often used when discussing mixtures of gases or solids, but could be used in liquids. Mole fraction is denoted by the Greek letter chi, χ. The formula to calculate mole fraction is

Formality

Formality is a less common concentration unit. It appears to have the same definition as molarity with the formula:

Notice how the only difference between formality and molarity is the letters F and M. The difference is formality disregards what happens to the solute after it is added to the solution. For example, if you take 1 mole of NaCl and add it to 1 liter of water, most people would say you have a 1 M solution of NaCl. What you actually have is a 1 M solution of Na+ and Cl ions. Formality is used when it matters what happens to the solute in the solution. The above solution is a 1 F solution of NaCl.

In solutions where the solute does not dissociate, such as sugar in water, the molarity and formality are the same.

Know Your Concentrations – Difference Between Molarity and Molality

M or m?Molarity and molality are both measurements dealing with concentration of solutions in chemistry. When you see a bottle marked with either a capital M or a lower-case m, what does it mean? Is there a difference?

Yes there is a difference.

Molarity is the most common concentration measurement and denoted by the capital letter M. Molarity is the number of moles of something per volume of mixture containing the something. In solutions, it is the number of moles of solute present per liter of solution.

A 1 M (or 1 molar) solution of NaCl contains one mole of sodium chloride for every liter of solution.

Molality is another concentration measurement. It is the number of moles of solute per unit mass of the solvent. In SI units, the unit of molality is mol/kg. Some texts use the unit ‘molal’, but the official unit is mol/kg.

For aqueous solutions (solutions where the solvent is water) around room temperature, the difference between molarity and molality is very slight. One kilogram of water at room temperature is very close to one liter.

The key points to remember:

M – Molarity – moles per volume of solution – unit: mol/L
m – molality – moles per kilogram of solvent – unit: mol/kg

How To Convert Between Units – Ladder Method

To define a physical quantity, you must first define a means to measure that physical quantity. Measuring means a method of calculating the quantity from other known quantities. People have developed standard quantities for this purpose. Science today uses an international system of units known as SI units. (SI comes from the French “Système International d’unités”). While SI is the standard for most cases, occasionally other systems are used. The old Imperial system is still in use in the United States for many common day to day uses. The metric system was the precursor to the modern SI system, but has some minor differences.

It is common to have to convert a measurement between measuring systems. This is done using conversion factors. An example of a conversion factor is

1 km = 1000 m

There are 1000 meters in 1 kilometer. If you want to know how many meters are in 3 kilometers, you use this conversion factor to calculate the result.

ladder method math 1

This is possible because you are just multiplying the measurement by 1. This can be seen by dividing both sides of the conversion factor equation by one of the units.

Divide both sides of the conversion factor by 1 km

unit conversion math 2
unit conversion math step 3

The same is true if you divide both sides by 1000 m

unit conversion math 4
unit conversion math 5

It doesn’t change the value of the measurement when you multiply by the conversion factor. It just changes the units the measurement is compared to. This method of unit conversion is called “Unit Cancelling” because the undesired unit is cancelled out by the conversion factor.

Take the 3 kilometer example above. The kilometer unit is cancelled out leaving only meters on both sides of the equation.

Occasionally it will be necessary to perform multiple conversions in a row to get the units you need on a measurement. Since all you are doing is multiplying the base measurement by 1, you can perform all of the conversions as one long chain of conversion factors. This method is known as the “Ladder Method”. Each conversion step is another run of a ladder to cancel out the undesired units.

For example, if you were to convert 18 km/hr to m/s, you would have to use the following conversion factors:

1000 m = 1 km
60 min = 1 hr
60 s = 1 min

The goal in this conversion is to end up with meters in the numerator and seconds in the denominator. Set up your conversions so the undesired units are cancelled out.

unit conversion math 6

I have marked the cancellation of each different undesired measurement in different colors to illustrate the ladder of calculations to arrive at the correct units. In this case, 18 km/hr = 5 m/s.

 

 

What Is a Jiffy?

Lightning striking a tree.

Lightning striking a tree in a jiffy. Jiffy was once slang for lightning. Credit: NOAA

I’ll be finished in a jiffy!

What does that mean? What is a jiffy anyway?

A jiffy is a measure of time. Sometime in the 18th Century, a jiffy was slang for ‘lightning’. In the 20th Century, American chemist, Gilbert Lewis proposed the jiffy should be the time it takes for light to travel one centimeter.

Light moves 3.0 x 1010 centimeters in one second. Therefore, light traverses one centimeter in 3.33×10-11 seconds or 33.3 picoseconds.

Electrical engineers use a jiffy as a measurement of the period of alternating current cycles. In the United States, AC power operates at 60 cycles per second. Period = 1/frequency, so a jiffy is 1/60 second or 17 milliseconds. In Europe and parts of Asia, AC power operates at 50 cycles/second. A jiffy there is equal to 0.02 seconds.

A jiffy is also a variable time in computer science. A jiffy is equal to a single clock tick between interrupts. A jiffy is on the order of 1 to 10 milliseconds.

What ever your scientific field, a jiffy is a really short amount of time.