Contoh Soal Hukum Dalton Dan Pembahasannya

by Jhon Lennon 43 views

Dalton's Law, guys, is a fundamental concept in chemistry that describes the behavior of gas mixtures. Understanding this law is crucial for anyone studying chemistry, especially when dealing with partial pressures. So, let's dive into some example problems and their solutions to help you grasp this concept better.

What is Dalton's Law?

Before we jump into the problems, let’s quickly recap what Dalton’s Law actually states. Dalton's Law of Partial Pressures states that the total pressure exerted by a mixture of non-reacting gases is equal to the sum of the partial pressures of the individual gases. Mathematically, it’s expressed as:

Ptotal = P1 + P2 + P3 + ... + Pn

Where:

  • Ptotal is the total pressure of the gas mixture.
  • P1, P2, P3, ..., Pn are the partial pressures of the individual gases in the mixture.

In simpler terms, if you have a container with multiple gases inside, each gas contributes to the overall pressure. The amount each gas contributes depends on how much of that gas is present, assuming they don't react with each other. Now that we've refreshed our understanding, let's tackle some example problems to see Dalton's Law in action. These examples will cover various scenarios you might encounter, from simple calculations to more complex situations involving mole fractions and gas volumes. Remember, the key to mastering Dalton's Law is practice, so work through these examples carefully and try to apply the principles to new problems. Keep in mind that understanding the ideal gas law (PV=nRT) is often helpful when dealing with Dalton's Law problems, as it allows you to relate pressure, volume, temperature, and the number of moles of gas. So, with these tools in your arsenal, let's jump into the first problem and see how we can apply Dalton's Law to solve it.

Example Problems and Solutions

Problem 1: Simple Partial Pressure Calculation

Problem: A container holds a mixture of nitrogen gas (N2) at a partial pressure of 0.6 atm and oxygen gas (O2) at a partial pressure of 0.3 atm. What is the total pressure inside the container?

Solution:

Using Dalton's Law:

Ptotal = PN2 + PO2 Ptotal = 0.6 atm + 0.3 atm Ptotal = 0.9 atm

So, the total pressure inside the container is 0.9 atm. See? Pretty straightforward!

Problem 2: Calculating Partial Pressure from Total Pressure and Mole Fraction

Problem: A gas mixture contains methane (CH4) and ethane (C2H6). The total pressure of the mixture is 1.5 atm. If the mole fraction of methane is 0.6, what is the partial pressure of ethane?

Solution:

First, find the mole fraction of ethane:

Xethane = 1 - Xmethane Xethane = 1 - 0.6 Xethane = 0.4

Now, calculate the partial pressure of ethane:

PEthane = Xethane * Ptotal PEthane = 0.4 * 1.5 atm PEthane = 0.6 atm

Thus, the partial pressure of ethane in the mixture is 0.6 atm.

Problem 3: Partial Pressure and the Ideal Gas Law

Problem: A 10.0 L container at 27°C contains 0.5 moles of hydrogen gas (H2) and 0.25 moles of nitrogen gas (N2). Calculate the partial pressure of each gas and the total pressure in the container.

Solution:

First, convert the temperature to Kelvin:

T(K) = T(°C) + 273.15 T(K) = 27 + 273.15 T(K) = 300.15 K

Now, use the Ideal Gas Law (PV = nRT) to find the partial pressure of each gas. The ideal gas constant (R) is 0.0821 L atm / (mol K).

For hydrogen gas (H2):

PH2V = nH2RT PH2 = (nH2RT) / V PH2 = (0.5 mol * 0.0821 L atm / (mol K) * 300.15 K) / 10.0 L PH2 ≈ 1.23 atm

For nitrogen gas (N2):

PN2V = nN2RT PN2 = (nN2RT) / V PN2 = (0.25 mol * 0.0821 L atm / (mol K) * 300.15 K) / 10.0 L PN2 ≈ 0.615 atm

Finally, calculate the total pressure:

Ptotal = PH2 + PN2 Ptotal = 1.23 atm + 0.615 atm Ptotal ≈ 1.845 atm

So, the partial pressure of hydrogen gas is approximately 1.23 atm, the partial pressure of nitrogen gas is approximately 0.615 atm, and the total pressure in the container is approximately 1.845 atm.

Problem 4: Dealing with Water Vapor Pressure

Problem: A gas is collected over water at 25°C. The total pressure of the collected gas is 760 torr. The vapor pressure of water at 25°C is 24 torr. What is the pressure of the dry gas?

Solution:

Using Dalton's Law, we know that the total pressure is the sum of the pressure of the dry gas and the vapor pressure of water:

Ptotal = Pdry gas + PH2O

We need to find the pressure of the dry gas, so rearrange the equation:

Pdry gas = Ptotal - PH2O Pdry gas = 760 torr - 24 torr Pdry gas = 736 torr

Therefore, the pressure of the dry gas is 736 torr. When collecting gases over water, it's crucial to remember to subtract the vapor pressure of water to get the actual pressure of the gas you're interested in.

Problem 5: Mole Fraction and Partial Pressure in a Multi-Component System

Problem: A gas mixture contains 20g of Neon (Ne), 30g of Argon (Ar), and 40g of Xenon (Xe) in a container with a total pressure of 2 atm at 27°C. Calculate the partial pressure of each gas.

Solution:

First, find the number of moles of each gas using their respective molar masses:

Molar mass of Ne = 20.18 g/mol Moles of Ne (nNe) = 20g / 20.18 g/mol ≈ 0.991 mol

Molar mass of Ar = 39.95 g/mol Moles of Ar (nAr) = 30g / 39.95 g/mol ≈ 0.751 mol

Molar mass of Xe = 131.29 g/mol Moles of Xe (nXe) = 40g / 131.29 g/mol ≈ 0.305 mol

Next, calculate the total number of moles in the mixture:

ntotal = nNe + nAr + nXe ntotal = 0.991 mol + 0.751 mol + 0.305 mol ntotal ≈ 2.047 mol

Now, find the mole fraction of each gas:

XNe = nNe / ntotal = 0.991 mol / 2.047 mol ≈ 0.484 XAr = nAr / ntotal = 0.751 mol / 2.047 mol ≈ 0.367 XXe = nXe / ntotal = 0.305 mol / 2.047 mol ≈ 0.149

Finally, calculate the partial pressure of each gas using Dalton's Law:

PNe = XNe * Ptotal = 0.484 * 2 atm ≈ 0.968 atm

Par = XAr * Ptotal = 0.367 * 2 atm ≈ 0.734 atm

PXe = XXe * Ptotal = 0.149 * 2 atm ≈ 0.298 atm

Therefore, the partial pressures are approximately:

Neon: 0.968 atm Argon: 0.734 atm Xenon: 0.298 atm

Tips for Solving Dalton's Law Problems

  1. Understand the Basics: Make sure you have a solid understanding of Dalton's Law and the Ideal Gas Law. These are your primary tools.
  2. Convert Units: Ensure all your units are consistent (e.g., temperature in Kelvin, pressure in atm, volume in liters).
  3. Identify Given Information: Clearly identify what information is given in the problem and what you need to find.
  4. Use Mole Fractions: When given the composition of a gas mixture, use mole fractions to find partial pressures.
  5. Account for Water Vapor: If collecting gas over water, remember to subtract the vapor pressure of water.
  6. Practice Regularly: The more you practice, the better you'll become at recognizing and solving these types of problems.

Conclusion

Dalton's Law is a fundamental concept in chemistry that helps us understand the behavior of gas mixtures. By working through these example problems and keeping the tips in mind, you'll be well-equipped to tackle any Dalton's Law problem that comes your way. Keep practicing, and you'll master it in no time!