Review of Measurement

<body> <p align="center"><a name="top"><font size="6"><b>Units</b></font></a></p> <div align="center"><center><table border="1" cellspacing="1" width="500" bordercolor="#000000"> <tr> <td align="center" width="20%"><a href="#english"><b>English System</b></a> </td> <td align="center" width="19%"><a href="#metric"><b>Metric System</b></a> </td> <td align="center" width="21%"><a href="#prefix"><strong>Metric System Prefixes</strong></a> </td> <td align="center" width="19%"><a href="#mass"><b>Mass vs. Weight</b></a> </td> </tr> <tr> <td align="center"><a href="#si"><b>SI Units</b></a> </td> <td align="center"><a href="#derivsi"><strong>Derived SI Units</strong></a> </td> <td align="center"><a href="#nonsi"><b>Non-SI Units</b></a> </td> <td align="center"><a href="#convers"><strong>Unit Conversions</strong></a> </td> </tr> </table> </center></div><hr> <p align="center"><a name="english"><b><i>The English System of Units</i></b></a></p> <p>There are<a name="english"> </a>several systems of units, each containing units for properties such as length, volume, weight, and time. In the <b>English system</b> the units are defined in an arbitrary way.</p> <div align="center"><center><table border="0" cellpadding="0" cellspacing="0" width="500" bordercolor="#FFFFFF"> <tr> <td colspan="6" width="92%"><b><i>Length: inch (in), foot (ft), yard (yd), mile (mi)</i></b> </td> </tr> <tr> <td width="8%"> </td> <td width="20%">12 in = 1 ft</td> <td width="8%"> </td> <td width="8%"> </td> <td width="8%"> </td> <td width="46%">5280 ft = 1 mi </td> </tr> <tr> <td width="8%"> </td> <td width="20%">3 ft = 1 yd </td> <td width="8%"> </td> <td width="8%"> </td> <td width="8%"> </td> <td width="46%">1760 yd = 1 mi </td> </tr> <tr> <td colspan="6" width="92%"><b><i>Volume: fluid ounce (oz), cup (c), pint (pt), quart (qt), gallon (gal)</i></b> </td> </tr> <tr> <td width="8%"> </td> <td width="20%">2 c = 1 pt </td> <td width="8%"> </td> <td width="8%"> </td> <td width="8%"> </td> <td width="46%">32 oz = 1 qt </td> </tr> <tr> <td width="8%"> </td> <td width="20%">2 pt = 1 qt </td> <td width="8%"> </td> <td width="8%"> </td> <td width="8%"> </td> <td width="46%">4 qt = 1 gal </td> </tr> <tr> <td colspan="6" width="92%"><b><i>Weight: ounce (oz), pound (lb), ton</i></b> </td> </tr> <tr> <td width="8%"> </td> <td width="20%">16 oz = 1 lb </td> <td width="8%"> </td> <td width="8%"> </td> <td width="8%"> </td> <td width="46%">2000 lb = 1 ton </td> </tr> <tr> <td colspan="6" width="92%"><b><i>Time: second (s), minute (min), hour (h), day (d), year (y)</i></b> </td> </tr> <tr> <td width="8%"> </td> <td width="20%">60 s = 1 min </td> <td width="8%"> </td> <td width="8%"> </td> <td width="8%"> </td> <td width="46%">24 h = 1 d </td> </tr> <tr> <td width="8%"> </td> <td width="20%">60 min = 1 h </td> <td width="8%"> </td> <td width="8%"> </td> <td width="8%"> </td> <td width="46%">365<sup>1</sup>/<sub>4</sub> d = 1 y <a name="prob1"></a></td> </tr> </table> </center></div><p align="right"> </p> <div align="center"><center><table border="5" cellpadding="10" width="100%" bordercolor="#B87333"> <tr> <td><em><strong>Practice Problem 1</strong></em><p>Convert 6.5 feet into inches. </p> <p><a href="http://chemed.chem.purdue.edu/~genchem/topicreview/bp/ch1/problems/ex1_1a.html"><em><strong>Click here to check your answer to Practice Problem 1</strong></em></a></p> <p><a href="http://chemed.chem.purdue.edu/~genchem/topicreview/bp/ch1/problems/ex1_1.html"><em><strong>Click here to see a solution to Practice Problem 1</strong></em></a></p> </td> </tr> </table> </center></div><p align="center"><a href="#top"><img src="graphics/top.gif" alt="Return to Top of Page" border="0" width="226" height="36" sgi_fullpath="/disk2/chemistry/genchem/public_html/topicreview/bp/ch1/graphics/top.gif"></a></p> <hr> <p align="center"><a name="metric"><b><i>The Metric System</i></b></a></p> <p>The <b>Metric System</b> is based on the fundamental units of measure for length, volume, and mass. </p> <div align="center"><center><table border="0" cellpadding="0" cellspacing="0"> <tr> <td>Length: </td> <td>meter (m)</td> <td> </td> </tr> <tr> <td>Volume: </td> <td>liter (L)</td> <td> </td> </tr> <tr> <td>Mass :</td> <td>gram (g)</td> <td> </td> </tr> </table> </center></div><p>Base units in the Metric System can be converted into units that are more appropriate for the quantity being measured by adding a prefix to the name of the base unit. The common metric prefixes are given below. </p> <p align="center"><a name="prefix"><b><i>Metric System Prefixes</i></b></a></p> <div align="center"><center><table border="0" cellpadding="0" cellspacing="0" width="500" bordercolor="#FFFFFF"> <tr> <td colspan="2" width="20%"><strong><i>Prefix</i></strong> </td> <td width="3%"> </td> <td align="center" colspan="2" width="15%"><strong><i>Symbol</i></strong> </td> <td width="62%"><strong><i>Meaning</i></strong> </td> </tr> <tr> <td width="8%"> </td> <td width="12%">femto- </td> <td width="3%"> </td> <td align="center" width="8%">f </td> <td width="8%"> </td> <td width="62%">x 1/1,000,000,000,000,000 (10<sup>-15</sup>)</td> </tr> <tr> <td width="8%"> </td> <td width="12%">pico- </td> <td width="3%"> </td> <td align="center" width="8%">p </td> <td width="8%"> </td> <td width="62%">x 1/1,000,000,000,000 (10<sup>-12</sup>) </td> </tr> <tr> <td width="8%"> </td> <td width="12%">nano- </td> <td width="3%"> </td> <td align="center" width="8%">n </td> <td width="8%"> </td> <td width="62%">x 1/1,000,000,000 (10<sup>-9</sup>) </td> </tr> <tr> <td width="8%"> </td> <td colspan="2" width="15%">micro- </td> <td align="center" width="8%">µ </td> <td width="8%"> </td> <td width="62%">x 1/1,000,000 (10<sup>-6</sup>) </td> </tr> <tr> <td width="8%"> </td> <td width="12%">milli- </td> <td width="3%"> </td> <td align="center" width="8%">m </td> <td width="8%"> </td> <td width="62%">x 1/1,000 (10<sup>-3</sup>) </td> </tr> <tr> <td width="8%"> </td> <td width="12%">centi- </td> <td width="3%"> </td> <td align="center" width="8%">c </td> <td width="8%"> </td> <td width="62%">x 1/100 (10<sup>-2</sup>) </td> </tr> <tr> <td width="8%"> </td> <td width="12%">deci- </td> <td width="3%"> </td> <td align="center" width="8%">d </td> <td width="8%"> </td> <td width="62%">x l/10(10<sup>-1</sup>) </td> </tr> <tr> <td width="8%"> </td> <td width="12%">kilo- </td> <td width="3%"> </td> <td align="center" width="8%">k </td> <td width="8%"> </td> <td width="62%">x 1,000 (10<sup>3</sup>) </td> </tr> <tr> <td width="8%"> </td> <td width="12%">mega- </td> <td width="3%"> </td> <td align="center" width="8%">M </td> <td width="8%"> </td> <td width="62%">x 1,000,000 (10<sup>6</sup>) </td> </tr> <tr> <td width="8%"> </td> <td width="12%">giga- </td> <td width="3%"> </td> <td align="center" width="8%">G </td> <td width="8%"> </td> <td width="62%">x 1,000,000,000 (10<sup>9</sup>) </td> </tr> <tr> <td width="8%"> </td> <td width="12%">tera- </td> <td width="3%"> </td> <td align="center" width="8%">T </td> <td width="8%"> </td> <td width="62%">x 1,000,000,000,000 (10<sup>12</sup>) </td> </tr> </table> </center></div><p>The base units of length and volume are linked in the metric system. By definition, a liter is equal to the volume of a cube exactly 10 cm tall, 10 cm long, and 10 cm wide. Because the volume of this cube is 1000 cubic centimeters and a liter contains 1000 milliliters, 1 milliliter is equivalent to 1 cubic centimeter. </p> <p align="center">1 mL = 1cm<sup>3</sup></p> <p>The base units of volume and weight are also linked. The gram was originally defined as the mass of 1 mL of water at 4 degrees Celsius. <a name="prob2"></a></p> <p align="center">1g = 1mL H<sub>2</sub>O at 4 °C</p> <div align="center"><center><table border="5" cellpadding="10" width="100%" bordercolor="#B87333"> <tr> <td><em><strong>Practice Problem 2:</strong></em><p>Convert 0.135 kilometers into meters. </p> <p><a href="problems/ex1_2a.html"><em><strong>Click here to check your answer to Practice Problem 2</strong></em></a></p> <p><a href="problems/ex1_2.html"><em><strong>Click here to see a solution to Practice Problem 2</strong></em></a></p> </td> </tr> </table> </center></div><p align="center"><a href="#top"><img src="graphics/top.gif" alt="Return to Top of Page" border="0" width="226" height="36" sgi_fullpath="/disk2/chemistry/genchem/public_html/topicreview/bp/ch1/graphics/top.gif"></a></p> <hr> <p align="center"><a name="mass"><b><i>Mass Versus Weight</i></b></a></p> <p><b>Mass</b> is a measure of the amount of matter in an object, so the mass of an object is constant.</p> <p><b>Weight</b> is a measure of the force of attraction of the earth acting on an object. The weight of an object is not constant. </p> <p>Mass is a more fundamental quantity than weight. There is no English equivalent to the verb <i>weigh</i> that can be used to describe what happens when the mass of an object is measured. You are therefore likely to encounter the terms <i>weigh</i> and <i>weight</i> for operations and quantities that are more accurately associated with the term <i>mass</i>.</p> <p align="center"><a href="#top"><img src="graphics/top.gif" alt="Return to Top of Page" border="0" width="226" height="36" sgi_fullpath="/disk2/chemistry/genchem/public_html/topicreview/bp/ch1/graphics/top.gif"></a></p> <hr> <p align="center"><a name="si"><font size="3"><b><i>SI Units of Measure</i></b></font></a></p> <p>In 1960 the <b>International System of Units</b> was proposed as a replacement for the Metric System. The seven base units for the SI system are given below.</p> <p align="center"><b><i>SI Base Units</i></b></p> <div align="center"><center><table border="0" cellpadding="0" cellspacing="0" width="500" bordercolor="#FFFFFF"> <tr> <td width="25%"><strong>Physical Quantity</strong> </td> <td width="10%"> </td> <td width="25%"><strong>Name of Unit</strong> </td> <td width="10%"> </td> <td width="25%"><strong>Symbol</strong> </td> </tr> <tr> <td width="25%">length </td> <td width="10%"> </td> <td width="25%">meter </td> <td width="10%"> </td> <td width="25%">m </td> </tr> <tr> <td width="25%">mass </td> <td width="10%"> </td> <td width="25%">kilogram </td> <td width="10%"> </td> <td width="25%">kg </td> </tr> <tr> <td width="25%">time </td> <td width="10%"> </td> <td width="25%">second </td> <td width="10%"> </td> <td width="25%">s </td> </tr> <tr> <td width="25%">temperature </td> <td width="10%"> </td> <td width="25%">kelvin </td> <td width="10%"> </td> <td width="25%">K </td> </tr> <tr> <td width="25%">electric current </td> <td width="10%"> </td> <td width="25%">ampere </td> <td width="10%"> </td> <td width="25%">D </td> </tr> <tr> <td width="25%">amount of substance </td> <td width="10%"> </td> <td width="25%">mole </td> <td width="10%"> </td> <td width="25%">mol </td> </tr> <tr> <td width="25%">luminous intensity </td> <td width="10%"> </td> <td width="25%">candela </td> <td width="10%"> </td> <td width="25%">cd </td> </tr> </table> </center></div><p align="center"><a href="#top"><img src="graphics/top.gif" alt="Return to Top of Page" border="0" width="226" height="36" sgi_fullpath="/disk2/chemistry/genchem/public_html/topicreview/bp/ch1/graphics/top.gif"></a></p> <hr> <p align="center"><a name="derived"><b><i>Derived Si Units</i></b></a></p> <p>The <a name="derivsi">units</a> of every measurement in the SI system must be derived from one or more of the seven base units. Some of the common derived SI units used in chemistry are given below. </p> <p align="center"><b><i>Common Derived SI Units in Chemistry</i></b></p> <div align="center"><center><table border="0" cellpadding="0" cellspacing="0" width="500" bordercolor="#FFFFFF"> <tr> <td colspan="4" width="31%"><b><i>Physical Quantity</i></b> </td> <td width="8%"> </td> <td colspan="3" width="30%"><b><i>Name of Unit</i></b> </td> <td> </td> <td valign="top" colspan="2" width="38%"><b><i>Symbol</i></b> </td> </tr> <tr> <td colspan="4" width="31%">density </td> <td width="8%"> </td> <td colspan="3" width="30%"> </td> <td width="8%"> </td> <td width="31%">kg/m<sup>3</sup> </td> </tr> <tr> <td colspan="4" width="31%">electric charge </td> <td width="8%"> </td> <td colspan="3" width="30%">coulomb </td> <td width="8%"> </td> <td width="31%">C (A · s) </td> </tr> <tr> <td colspan="4" width="31%">electric potential </td> <td width="8%"> </td> <td colspan="3" width="30%">volt </td> <td width="8%"> </td> <td width="31%">V (J/C) </td> </tr> <tr> <td colspan="4" width="31%">energy </td> <td width="8%"> </td> <td colspan="3" width="30%">joule </td> <td width="8%"> </td> <td width="31%">J (kg-m<sup>2</sup>/s<sup>2</sup>) </td> </tr> <tr> <td colspan="4" width="31%">force </td> <td width="8%"> </td> <td colspan="3" width="30%">newton </td> <td width="8%"> </td> <td width="31%">N (kg-m/s<sup>2</sup>) </td> </tr> <tr> <td colspan="4" width="31%">frequency </td> <td width="8%"> </td> <td colspan="3" width="30%">hertz </td> <td width="8%"> </td> <td width="31%">Hz (s<sup>-1</sup>) </td> </tr> <tr> <td colspan="4" width="31%">pressure </td> <td width="8%"> </td> <td colspan="3" width="30%">pascal </td> <td width="8%"> </td> <td width="31%">Pa (N/m<sup>2</sup>) </td> </tr> <tr> <td colspan="4" width="31%">velocity (speed) </td> <td width="8%"> </td> <td colspan="3" width="30%">meters per second </td> <td width="8%"> </td> <td width="31%">m/s </td> </tr> <tr> <td colspan="4" width="31%">volume </td> <td width="8%"> </td> <td colspan="3" width="30%">cubic meter </td> <td width="8%"> </td> <td width="31%">m<sup>3</sup> </td> </tr> </table> </center></div><p align="center"><a href="#top"><img src="graphics/top.gif" alt="Return to Top of Page" border="0" width="226" height="36" sgi_fullpath="/disk2/chemistry/genchem/public_html/topicreview/bp/ch1/graphics/top.gif"></a></p> <hr> <p align="center"><a name="nonsi"><b><i>Non-SI Units</i></b></a></p> <p>Strict adherence to SI units would require changing directions such as "add 250 mL of water to a 1-L beaker" to "add 0.00025 cubic meters of water to an 0.001-m<sup>3</sup> container." Because of this, a number of units that are not strictly acceptable under the SI convention are still in use. Some of these non-SI units are given below. </p> <p align="center"><b><i>Non-SI Units in Common Use</i></b></p> <div align="center"><center><table border="0" cellpadding="0" cellspacing="0" width="500" bordercolor="#FFFFFF"> <tr> <td colspan="4" width="31%"><b><i>Physical Quantity</i></b> </td> <td width="8%"> </td> <td colspan="2" width="18%"><b><i>Name of Unit</i></b> </td> <td> </td> <td colspan="2" width="43%"><b><i>Symbol</i></b> </td> </tr> <tr> <td width="8%"> </td> <td colspan="2" width="19%">volume </td> <td width="4%"> </td> <td width="8%"> </td> <td width="8%">liter </td> <td width="11%"> </td> <td width="5%"> </td> <td width="38%">L (10<sup>-3</sup> m<sup>3</sup>) </td> </tr> <tr> <td width="8%"> </td> <td width="11%">length </td> <td width="9%"> </td> <td width="4%"> </td> <td width="8%"> </td> <td colspan="2" width="18%">angstrom </td> <td width="5%"> </td> <td width="38%">D (0.1 nm) </td> </tr> <tr> <td width="8%"> </td> <td colspan="2" width="19%">pressure </td> <td width="4%"> </td> <td width="8%"> </td> <td colspan="2" width="18%">atmosphere </td> <td width="5%"> </td> <td width="38%">atm (101.325 kPa) </td> </tr> <tr> <td width="8%"> </td> <td width="11%"> </td> <td width="9%"> </td> <td width="4%"> </td> <td width="8%"> </td> <td width="8%">torr </td> <td width="11%"> </td> <td width="5%"> </td> <td width="38%">mmHg (133.32 Pa) </td> </tr> <tr> <td width="8%"> </td> <td width="11%">energy </td> <td width="9%"> </td> <td width="4%"> </td> <td width="8%"> </td> <td colspan="2" width="18%">electron volt </td> <td width="5%"> </td> <td width="38%">eV (1.601 x 10<sup>-19</sup> J) </td> </tr> <tr> <td width="8%"> </td> <td colspan="2" width="19%">temperature </td> <td width="4%"> </td> <td width="8%"> </td> <td colspan="3" width="23%">degree Celsius </td> <td width="38%">EC (K - 273.15) </td> </tr> <tr> <td width="8%"> </td> <td colspan="2" width="19%">concentration </td> <td width="4%"> </td> <td width="8%"> </td> <td colspan="2" width="18%">molarity </td> <td width="5%"> </td> <td width="38%"><i>M</i> (mol/L) </td> </tr> </table> </center></div><p align="center"><a href="#top"><img src="graphics/top.gif" alt="Return to Top of Page" border="0" width="226" height="36" sgi_fullpath="/disk2/chemistry/genchem/public_html/topicreview/bp/ch1/graphics/top.gif"></a></p> <hr> <p align="center"><a name="convers"><strong>Unit Conversions</strong></a></p> <div align="center"><center><table border="0" cellpadding="0" cellspacing="0" width="300"> <tr> <td width="20%"><u>Length </u></td> <td align="center" width="50%"> </td> </tr> <tr> <td width="50%">1 m = 1.094 yd </td> <td align="center" width="50%">1 yd = 0.9144</td> </tr> <tr> <td width="20%"><u>Volume</u> </td> <td align="center" width="50%"> </td> </tr> <tr> <td width="20%">1 L = 1.057 qt </td> <td align="center" width="50%">1 qt = 0.9464</td> </tr> <tr> <td width="20%"><u>Mass </u><a name="prob3"></a></td> <td align="center" width="50%"> </td> </tr> <tr> <td width="20%">1 g = 0.002205 lb </td> <td align="center" width="50%">1 lb = 453.6 g </td> </tr> </table> </center></div><p align="right"> </p> <div align="center"><center><table border="5" cellpadding="10" width="100%" bordercolor="#B87333"> <tr> <td><em><strong>Practice Problem 3</strong></em><p>The record for the Kentucky Derby is held by Secretariat, who ran the 10 furlongs in 1 minute, 59.4 seconds. Calculate his average speed in miles per hour. </p> <p><a href="problems/ex1_6a.html"><em><strong>Click here to check your answer to Practice Problem 3</strong></em></a></p> <p><a href="problems/ex1_6.html" name="prob4"><em><strong>Click here to see a solution to Practice Problem 3</strong></em></a></p> </td> </tr> </table> </center></div><p align="right"> </p> <div align="center"><center><table border="5" cellpadding="10" width="100%" bordercolor="#B87333"> <tr> <td><em><strong>Practice Problem 4</strong></em><p>Calculate the volume in liters of a cubic container 0.500 meter tall. </p> <p><a href="problems/ex1_7a.html"><em><strong>Click here to check your answer to Practice Problem 4</strong></em></a></p> <p><a href="problems/ex1_7.html" name="prob5"><em><strong>Click here to see a solution to Practice Problem 4</strong></em></a></p> </td> </tr> </table> </center></div><p align="right"> </p> <div align="center"><center><table border="5" cellpadding="10" width="100%" bordercolor="#B87333"> <tr> <td><em><strong>Practice Problem 5</strong></em><p>What is the value of a gold ingot 20.0 cm long by 8.5 cm wide by 6.0 cm tall, if the mass of a cubic centimeter of gold is 19.3 grams and the price of gold is $356 per ounce? </p> <p><a href="problems/ex1_8a.html"><em><strong>Click here to check your answer to Practice Problem 5</strong></em></a></p> <p><a href="problems/ex1_8.html"><em><strong>Click here to see a solution to Practice Problem 5</strong></em></a></p> </td> </tr> </table> </center></div><p align="right"> </p> <p align="center"><a href="#top"><img src="graphics/top.gif" alt="Return to Top of Page" border="0" width="226" height="36" sgi_fullpath="/disk2/chemistry/genchem/public_html/topicreview/bp/ch1/graphics/top.gif"></a></p> <hr> <p><img src="http://chemed.chem.purdue.edu/Count.cgi?df=topicrevunits.dat"></p> </body>