Understanding the Different Gas Laws
Identify Charles's Law. Charles's law states that the volume and the temperature of a gas in Kelvin are directly proportional to each other. This means if the volume of a gas increases, its temperature will increase as well. If the volume of a gas decreases, its temperature will also decrease. Keep in mind that the temperature units have to be in Kelvin for the volume and the temperature to be proportional. If they are in Celsius or Fahrenheit, you will have to convert them to Kelvin to use the formula. The temperature of the gas and the number of moles of the gas are kept constant. The formula for this law is V 1 / T 1 = V 2 / V 2 {\displaystyle V_{1}/T_{1}=V_{2}/V_{2}} {\displaystyle V_{1}/T_{1}=V_{2}/V_{2}}.
Identify Boyle's Law. Boyle's law states that the gas pressure and the volume of a gas are inversely proportional to each other. This means when the gas pressure increases, the volume will decrease. When the gas pressure decreases, the volume will increase. The number of moles of the gas and the temperature are kept constant. The formula for this law is P 1 V 1 = P 2 V 2 {\displaystyle P_{1}V_{1}=P_{2}V_{2}} {\displaystyle P_{1}V_{1}=P_{2}V_{2}}.
Identify Gay-Lussac's law. Gay-Lussac's law states that the gas pressure and the temperature of a gas are directly proportional to each other. When the gas pressure increases, the temperature will also increase and get warmer. When the gas pressure decreases, the temperature becomes cooler. The volume of the gas and the number of moles are kept constant. The formula for this law is P 1 / T 1 = P 2 / T 2 {\displaystyle P_{1}/T_{1}=P_{2}/T_{2}} {\displaystyle P_{1}/T_{1}=P_{2}/T_{2}}.
Identify the combined gas law. The combined gas law is all of the previous laws combined. It establishes that the pressure of a gas and the volume of a gas are inversely proportional to each other, and they are each directly proportional to the temperature of the gas. The formula for this law is P 1 V 1 / T 1 = P 2 V 2 / T 2 {\displaystyle P_{1}V_{1}/T_{1}=P_{2}V_{2}/T_{2}} {\displaystyle P_{1}V_{1}/T_{1}=P_{2}V_{2}/T_{2}}.
Identify the ideal gas law. This formula adds the relationship between the number of moles of the gas with the other elements (pressure, volume, and temperature). The previous gas laws compared two gases together, whereas this formula only compares the characteristics of one gas. The formula for this law is P V = n R T {\displaystyle PV=nRT} {\displaystyle PV=nRT}. P {\displaystyle P} P stands for the gas pressure. The standard units for gas pressure are mmHg (millimeters of mercury), kPa (kilopascals), torr, and atm (atmosphere). V {\displaystyle V} V stands for the gas's volume. The standard units for volume are in liters, but you can convert the volume to smaller units, such as the milliliter. n {\displaystyle n} n stands for the number of moles of a gas. A mole is 6.02 ∗ 10 23 {\displaystyle 6.02*10^{23}} {\displaystyle 6.02*10^{23}} particles. When solving these problems, you may need to convert the number of particles to moles. R {\displaystyle R} R is the ideal gas constant. This number is different depending on which units of pressure (mmHg, kPa, atm) you use. T {\displaystyle T} T is the temperature of the gas. In science, you need to always convert the temperature to Kelvin.
Determining Which Formula to Use
Determine if the problem tells you to solve for the volume or temperature of one gas. If the problem gives you information on the volume of one gas and the temperatures of both gases, use Charles's law. If the problem gives you the volumes of both gases but only one temperature value, use Charles's law too. This formula allows you to solve for the volume (measured in liters) or the temperature (measured in Kelvin) of a gas. The pressure and the amount of gas are the constant variables. Either the volume or temperature value is being changed.
Determine if the problem tells you to solve for the pressure or volume of one gas. If the problem gives you information on the pressure of one gas and two volumes, use Boyle's law. Likewise, if the problem gives you the pressures of both gases but only one volume value, use Boyle's law. This law helps you solve for either the pressure (measured in atm, mmHg, or kPa) or the volume (measured in liters) of a gas. The temperature and the amount of gas are the constant variables. Either the pressure or volume value is being changed.
Determine if the problem tells you to solve for the pressure or temperature of one gas. If the problem gives you information on the pressure of one gas and two temperature values, use Gay-Lussac's law. Likewise, if the problem gives you the temperature of two gasses and one pressure value, use Gay-Lussac's law. This law helps you solve for either the pressure (measured in atm, mmHg, or kPa) or the temperature (measured in Kelvin) of a gas. The volume and the amount of gas are the constant variables. Either the pressure or temperature is being changed.
Determine if the problem tells you to solve for a pressure, temperature, or volume variable. The combined gas law equation will usually give you two pressure, temperature, or volume variables. Two of these will be changed in the equation. This equation compares a gas when some of its conditions are changed. For example, the problem may ask you to find the volume of a 3.22-liter gas after its temperature changes from 23 degrees Celsius to 45 degrees Celsius. Because two variables are changing (both temperature and volume in this case), you use the combined gas law.
Determine if the problem tells you to solve for one of the variables in the PV = nRT equation. If the problem gives you one of each variable (and not two pressure, two temperature, or two-volume values), you are likely dealing with an ideal gas law problem. Additionally, if the problem tells you to solve for the amount of gas in moles, you will need to use this formula to solve it. An ideal gas law problem may look like this: "1.3 mol of Argon gas is placed in a container at 27 C at a pressure of 725 torr. What is the volume of the container in mL?" Notice that the problem doesn't contain more than one temperature and pressure value. It also includes the n value (representing the amount of a gas in moles). This variable is not seen in any of the other gas law equations, so the only one that you should use is the ideal gas law.
Solving Gas Law Problems
Read the problem and identify which variables the problem talks about. Use your knowledge of each formula to determine which one to use. Determine which variables are changed. For example, if the problem tells you to solve for a temperature value after the pressure has increased/decreased, you need to use Gay-Lussac's law.
Substitute the appropriate values into the equation. Substitute the known values/numbers into the equation. Make sure to read carefully and convert units to standard ones. For example, if the problem gives you a temperature value in Celsius, convert that to Kelvin first, because the formula only works with Kelvin.
Move the known values to one side and the variable to the other side. Using your algebra skills, use arithmetic to move the known values to one side and the variable to another. For example, if you get 200 m l / 0.25 m o l = V 2 / 1.0 m o l {\displaystyle 200ml/0.25mol=V_{2}/1.0mol} {\displaystyle 200ml/0.25mol=V_{2}/1.0mol} after substituting your values in, cross multiply. Multiply 200 m l {\displaystyle 200ml} {\displaystyle 200ml} by 1.0 m o l {\displaystyle 1.0mol} {\displaystyle 1.0mol} and 0.25 m o l {\displaystyle 0.25mol} {\displaystyle 0.25mol} by V 2 {\displaystyle V_{2}} {\displaystyle V_{2}}. You will get 200 m l {\displaystyle 200ml} {\displaystyle 200ml} equals 0.25 V 2 {\displaystyle 0.25V_{2}} {\displaystyle 0.25V_{2}}. Next, you would divide each side of the equation by 0.25 {\displaystyle 0.25} 0.25 to cancel the numbers out. 200 / 0.25 m l = V 2 {\displaystyle 200/0.25ml=V_{2}} {\displaystyle 200/0.25ml=V_{2}}. This value is 800 m l {\displaystyle 800ml} {\displaystyle 800ml}.
Round to the correct significant figures. Brush up on your knowledge of significant figures to ensure you won't get a few points off for a minor reason on your next chemistry test. There are a few rules in rounding to some significant figures in chemistry that you need to follow. Do not remove or round off any non-zero digits. 12345 has 5 digits in total, and they are all significant. Keep zeroes to the right of the decimal point. 1234 and 1234.0 are different because 1234.0 has 5 significant figures, and 1234 only has four. Remove zeroes to the left of the decimal point (and zeroes in front of non-zero integers). For example, you would remove all of the zeroes from the number 0.009, leaving it with only one' significant figure. However, you would keep the zero between 3 and 9 in the number 0.5309 {\displaystyle 0.5309} {\displaystyle 0.5309}. You would still remove the 0 in front of the decimal point and the number 5, leaving the number with 4 significant figures (5, 3, 0, and 9). When adding and subtracting, your value should match the number with the least amount of decimal places in the equation. For example, when adding 0.38 + 5.5 {\displaystyle 0.38+5.5} {\displaystyle 0.38+5.5}, your answer would only have 1 decimal place, matching 5.5 {\displaystyle 5.5} {\displaystyle 5.5}. Instead of the answer being 5.88 {\displaystyle 5.88} {\displaystyle 5.88}, it would be 5.9 {\displaystyle 5.9} {\displaystyle 5.9}. When multiplying and dividing, your value should match the number with the least amount of significant figures. This is different than the same number of decimal places. For example, when multiplying 0.38 ∗ 5.50 {\displaystyle 0.38*5.50} {\displaystyle 0.38*5.50}, your answer would only have 2 significant figures, matching 0.38 {\displaystyle 0.38} {\displaystyle 0.38}. Instead of the answer being 2.09 {\displaystyle 2.09} {\displaystyle 2.09}, it would be 2.1 {\displaystyle 2.1} {\displaystyle 2.1}.
Check your units. After you solve the problem, the units should match which variable you are solving for. If you have extra units you haven't canceled out (or the wrong units), you need to go back and redo your work. For example, you need to have temperature units in Kelvin. If you accidentally forgot to convert your temperature units to Kelvin while solving with these formulas, your answer would be incorrect. Your volume units need to be in liters or milliliters. Your pressure units need to be in mmHg, torr, kPa, or atm. It's a good idea to convert your pressure units to match what the problem is asking. For example, if the problem gives you the pressure in mmHg but the problem tells you to answer kPa, it's easier to convert the units to kPa beforehand. The amount of gas is represented with moles. Sometimes, the problem only gives you the amount of particles, so you will need to convert that value to moles. A mole is 6.02 ∗ 10 23 {\displaystyle 6.02*10^{23}} {\displaystyle 6.02*10^{23}} particles. If the problem asks you to find the amount of gas in grams (and you have found the n value in the ideal gas law equation), find the gas's atomic mass (seen on the periodic table). This unit will be in grams per mol (g/mol). Next, multiply the n-value (units in moles) by the atomic mass (g/mol) to find the number of grams. The moles in the equation will cancel out, leaving you with the amount of grams.
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