Chem 1000 Gases

• Be able to convert among the common units of pressure.

🔑 Key Units:

• 1 atm = 760 mmHg = 760 torr = 101.325 kPa = 1.01325 bar = 14.7 psi

✅ What to Know:

• Memorize the conversions.

• You’ll often need to convert units when using the ideal gas law.

✍ Example:

Convert 1.2 atm to mmHg
→ 1.2 atm×760 mmHg1 atm=912 mmHg1.2 \, \text{atm} \times \frac{760 \, \text{mmHg}}{1 \, \text{atm}} = 912 \, \text{mmHg}1.2atm×1atm760mmHg​=912mmHg

🟡 YouTube Recommended?
Not essential. I can explain this fully here. But search “Pressure unit conversions chemistry” if you’re a visual learner.

• Explain the operation of a mercury barometer.

• Learn Boyle's law both mathematically and graphically and be able to use it in calculations.

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3. Boyle’s Law (Pressure–Volume Relationship) Equation: P1V1=P2V2(at constant T and n)P_1 V_1 = P_2 V_2 \quad \text{(at constant T and n)}P1​V1​=P2​V2​(at constant T and n) Graph:

• Inversely proportional → hyperbola.

• As pressure increases, volume decreases.

✍ Example:

A gas at 2.0 L and 1.0 atm is compressed to 1.0 L. What’s the new pressure?

P2=P1V1V2=1.0×2.01.0=2.0 atmP_2 = \frac{P_1 V_1}{V_2} = \frac{1.0 \times 2.0}{1.0} = 2.0 \, \text{atm}P2​=V2​P1​V1​​=1.01.0×2.0​=2.0atm

• Learn Charles's law both mathematically and graphically and be able to use it in calculations.

4. Charles’s Law (Volume–Temperature Relationship) Equation: V1T1=V2T2(at constant P and n)\frac{V_1}{T_1} = \frac{V_2}{T_2} \quad \text{(at constant P and n)}T1​V1​​=T2​V2​​(at constant P and n)

Temperatures must be in Kelvin.

✍ Example:

A gas at 300 K has volume 2.0 L. What is the volume at 600 K?

V2=V1T2T1=2.0×600300=4.0 LV_2 = \frac{V_1 T_2}{T_1} = \frac{2.0 \times 600}{300} = 4.0 \, \text{L}V2​=T1​V1​T2​​=3002.0×600​=4.0L

🟡 YouTube optional, but not necessary.

• Discuss the significance of the absolute zero of temperature and be able to convert between Celsius and Kelvin temperatures.

5. Absolute Zero & Celsius ↔ Kelvin Conversion

• Absolute zero = 0 K = –273.15 °C (theoretical point of zero kinetic energy).

• Conversion:

T(K)=T(°C)+273.15T(K) = T(°C) + 273.15T(K)=T(°C)+273.15 ✍ Example:

25°C = 25+273.15=298.15 K25 + 273.15 = 298.15 \, K25+273.15=298.15K

🟢 YouTube? No need. Easy to explain here.

• State and be able to use Avogadro's law.

6. Avogadro’s Law Equation: V1n1=V2n2(at constant T and P)\frac{V_1}{n_1} = \frac{V_2}{n_2} \quad \text{(at constant T and P)}n1​V1​​=n2​V2​​(at constant T and P)

→ Volume is directly proportional to moles of gas.

• Solve for one of P, V, n, or T when given values of the other three for an ideal gas.

Equation: PV=nRTPV = nRTPV=nRT

Where:

• P = pressure (atm)

• V = volume (L)

• n = moles

• R = 0.0821 L·atm/mol·K

• T = temperature (K)

🟢 Super important. Learn it well.

8. Combined Gas Law (Rearranging Variables)

If R is constant, use:

P1V1T1=P2V2T2\frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2}T1​P1​V1​​=T2​P2​V2​​

🟢 Good YouTube topic. Search: “Combined gas law tutorial”

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• Obtain the value of one final variable (P, V, n, or T), given the values of the other final variables and of all the initial variables, excluding those that remain unchanged, in the ideal gas law.

• Use alternate versions of the ideal gas law for calculating molar masses of gases and determining gas densities.

• Solve stoichiometry problems involving gases.

• Solve problems involving mixtures of gases with either the ideal gas law or Dalton's law of partial pressures.

• Compute the pressure of gases collected over water.

• State the postulates and the basic mathematical relationships of the kinetic molecular theory of gases.

• Demonstrate that the kinetic energy of molecules depends only on the temperature of the gas.

• Compute molecular velocities and explain effect of molar mass and temperature on molecular speed distributions.

• Explain the phenomena of effusion; compute relative effusion rates and apply Graham's law

• Explain why real gases differ from ideal gases and how the differences lead to the van der Waals equation. Know under what conditions gases are most nearly ideal