CHEM 370 Lecture Slides

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<h2 style = "text-align: left; font-weight: bold; margin-left: 40px; font-size: 54px; margin-top: 50px;">Units and Significant Digits</h2>

.image-credit[Public Domain [image](https://en.wikipedia.org/wiki/File:SI_Illustration_Base_Units_and_Constants_Colour_Full.svg).]

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# Dimensional Analysis

> The analysis of the relationships between values through identification of their base quantities (such as length, mass, time, and electric current) and units of measure (such as miles vs. kilometres, or pounds vs. kilograms).  These *dimensions* can be tracked to perform calculations and conversions.

**A** ***value*** **is made up of:**

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# Prefixes

.image-credit[David Harvey / [Analytical Chemistry 2.1](https://chem.libretexts.org/Bookshelves/Analytical_Chemistry/Book%3A_Analytical_Chemistry_2.1_%28Harvey%29) / [CC BY-SA 4.0](https://creativecommons.org/licenses/by-sa/3.0/at/deed.en)]

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# Units: What is a 'kilogram'?

**Original definition:** mass of 1 L water

**New definition:** Defined in terms of $h$ (and $c$, $\Delta\_{{v}\_{\text{Cs}}}$).

???

$c = 2.99 \times 10^{8} m/s$

$\Delta\_{{v}\_{\text{Cs}}} = $

$h = 6.62607015 \times 10^{−34} $ J s = kg m$^2$ / s

> The kilogram, symbol kg, is the SI unit of mass. It is defined by taking the fixed numerical value of the Planck constant h to be 6.62607015×10−34 when expressed in the unit J⋅s, which is equal to kg⋅m2⋅s−1, where the metre and the second are defined in terms of c and ΔνCs

> The second is defined as being equal to the time duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the fundamental unperturbed ground-state of the caesium-133 atom

> The metre is currently defined as the length of the path travelled by light in a vacuum in 1/299 792 458 of a second. The metre was originally defined in 1793 as one ten-millionth of the distance from the equator to the North Pole along a great circle, so the Earth's circumference is approximately 40000 km.

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# Units: Base SI Units

All units can be traced back to the **fundamental base SI units**.

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# Units: Common Units

Many units in use are either *derived SI units* or non-SI units (even in science!).

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# Dimensional Analysis

Most calculations can be solved using *dimensional analysis*.

Use conversions as needed to multiply until the correct value is obtained.

**A** ***value*** **is made up of:**

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# Significant Figures

> Tell other scientists about your *uncertainty*.

The number of significant figures in a measurement is the number of digits known exactly plus one digit whose value is uncertain.

This is one of the ways chemists communicate. (Remember this course is about the Analytical Perspective!)

???

Example: reading a balance

Example: determining sigfigs.

- non-zeros always significant!
  - Zeros *between* numbers *before decimal point* are significant.
  - After decimal point, any zero following a number is significant
  - Logs are unusual: numbers before decimal indicate *power of 10* and are **NOT** significant; only numbers after decimal are significant.
  - If in doubt conver to scientific notation!
  - Exact quantities have infinite sig figs!

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# Significant Digits: Caculations

- Addition and Subtraction: round to common decimal place - convert to same power of 10 first!
<img src="./img/chapter-1C/sigfigs_add-subtract.png" style = "height:125px; margin-left: auto; margin-right: auto; display: block;"> <img src="./img/chapter-1C/sigfigs_add-subtract-scinotation.png" style = "height:125px; margin-left: auto; margin-right: auto; display: block;">

- Multiplication and Division: round to least number of significant digits

- Note these are general rules that *usually* work!

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# An example

**You have made a sulfate stock solution by placing 0.2381 g of sodium sulfate into 1.000 L of water.  What is the sulfate concentration in mg/L?**

- You should always provide appropriate significant digits in your work.  When doing calculations, keep as many digits as possible until the last step to avoid round-off errors.
- When rounding, if last digit >5 round up; if < 5 round down; if 5, round up half the time and down half the time.
  - To be rigorous about this: round to nearest even number!