Soal Hukum Dalton Dan Jawabannya: Contoh Soal Dan Pembahasan

by Jhon Lennon 61 views

Hey guys! Are you struggling with Dalton's Law? No worries, you're not alone! Dalton's Law, a fundamental concept in chemistry, often appears in various problem sets. To help you master this topic, let’s dive into some example questions and their detailed solutions. This guide is designed to make understanding Dalton's Law easier and more practical. So, let’s get started and unravel the complexities of partial pressures together!

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. In simpler terms, if you have a container filled with different gases, the total pressure inside the container is just the sum of the pressures each gas would exert if it were alone in the container. The formula for Dalton's Law is:

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

Where:

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

Understanding this basic principle is crucial for tackling problems related to Dalton's Law. Remember, this law applies to ideal gases, meaning we assume there are no intermolecular interactions between the gas molecules. Now that we've refreshed our understanding, let's move on to some example problems.

Example Problems and Solutions

Let's work through some examples of Dalton's Law problems with detailed explanations. Each problem will illustrate a different aspect of the law, helping you to build a solid understanding. Understanding the concept is half the battle, so let's try to solve some problems to solidify our understanding of Dalton's Law.

Problem 1

A container holds 2.0 moles of nitrogen gas (N2) and 3.0 moles of oxygen gas (O2) at a temperature of 25°C. The total pressure in the container is 5.0 atm. What is the partial pressure of each gas?

Solution

First, we need to determine the mole fraction of each gas. The mole fraction is the ratio of the number of moles of a particular gas to the total number of moles of all gases in the mixture.

  • Mole fraction of N2 (XN2) = moles of N2 / (moles of N2 + moles of O2) = 2.0 / (2.0 + 3.0) = 2.0 / 5.0 = 0.4
  • Mole fraction of O2 (XO2) = moles of O2 / (moles of N2 + moles of O2) = 3.0 / (2.0 + 3.0) = 3.0 / 5.0 = 0.6

Now, we can find the partial pressure of each gas by multiplying its mole fraction by the total pressure:

  • Partial pressure of N2 (PN2) = XN2 * Ptotal = 0.4 * 5.0 atm = 2.0 atm
  • Partial pressure of O2 (PO2) = XO2 * Ptotal = 0.6 * 5.0 atm = 3.0 atm

So, the partial pressure of nitrogen gas is 2.0 atm, and the partial pressure of oxygen gas is 3.0 atm. You can verify that the sum of the partial pressures equals the total pressure: 2.0 atm + 3.0 atm = 5.0 atm. Always double-check your work to ensure that the math is correct.

Problem 2

A gas mixture contains helium (He), neon (Ne), and argon (Ar). The partial pressure of He is 200 torr, Ne is 300 torr, and the total pressure of the mixture is 800 torr. What is the partial pressure of Ar?

Solution

Using Dalton's Law, we know that the total pressure is the sum of the partial pressures of all the gases:

Ptotal = PHe + PNe + PAr

We can rearrange this equation to solve for the partial pressure of Ar:

PAr = Ptotal - PHe - PNe

Now, plug in the given values:

PAr = 800 torr - 200 torr - 300 torr = 300 torr

Therefore, the partial pressure of argon is 300 torr. Remember to pay attention to the units. In this case, the total pressure and partial pressures are given in torr, so the answer is also in torr.

Problem 3

In a closed container, there are 4 grams of hydrogen gas (H2) and 32 grams of oxygen gas (O2) at 27°C. The total pressure of the mixture is 3 atm. Calculate the partial pressure of each gas.

Solution

First, we need to convert the mass of each gas to moles:

  • Moles of H2 = mass of H2 / molar mass of H2 = 4 g / 2 g/mol = 2 moles
  • Moles of O2 = mass of O2 / molar mass of O2 = 32 g / 32 g/mol = 1 mole

Next, find the mole fraction of each gas:

  • XH2 = moles of H2 / (moles of H2 + moles of O2) = 2 / (2 + 1) = 2/3
  • XO2 = moles of O2 / (moles of H2 + moles of O2) = 1 / (2 + 1) = 1/3

Now, calculate the partial pressure of each gas:

  • PH2 = XH2 * Ptotal = (2/3) * 3 atm = 2 atm
  • PO2 = XO2 * Ptotal = (1/3) * 3 atm = 1 atm

Thus, the partial pressure of hydrogen gas is 2 atm, and the partial pressure of oxygen gas is 1 atm. Always make sure to include units in your final answer!

Problem 4

A container has a volume of 10.0 L and contains nitrogen gas at a pressure of 2.0 atm and oxygen gas at a pressure of 1.0 atm. If the temperature is kept constant, what is the total pressure in the container?

Solution

This is a straightforward application of Dalton's Law. Since we already have the partial pressures of each gas, we simply add them together to find the total pressure:

Ptotal = PN2 + PO2

Plug in the values:

Ptotal = 2.0 atm + 1.0 atm = 3.0 atm

Therefore, the total pressure in the container is 3.0 atm. No need to overcomplicate things; Dalton's Law can be very simple to use when you already have the partial pressures.

Problem 5

20 L flask at 27°C contains a mixture of N2 and H2. The total pressure is 2 atm. If the partial pressure of H2 is 1.2 atm, calculate the mass of N2 present in the flask.

Solution

First, let's find the partial pressure of N2:

Ptotal = PN2 + PH2

So,

PN2 = Ptotal - PH2 = 2 atm - 1.2 atm = 0.8 atm

Now, we can use the ideal gas law to find the number of moles of N2:

PV = nRT

Where:

  • P = pressure (in atm)
  • V = volume (in L)
  • n = number of moles
  • R = ideal gas constant (0.0821 L atm / (mol K))
  • T = temperature (in K)

Convert the temperature to Kelvin:

T = 27°C + 273.15 = 300.15 K

Now, solve for n:

n = (PV) / (RT) = (0.8 atm * 20 L) / (0.0821 L atm / (mol K) * 300.15 K) ≈ 0.65 moles

Finally, calculate the mass of N2:

Mass of N2 = moles of N2 * molar mass of N2 = 0.65 moles * 28 g/mol ≈ 18.2 grams

Therefore, the mass of N2 present in the flask is approximately 18.2 grams. Make sure to use the correct units and the ideal gas constant value for accurate results.

Tips for Solving Dalton's Law Problems

  1. Understand the Basics: Make sure you have a solid understanding of Dalton's Law and the concept of partial pressures. Know the formula Ptotal = P1 + P2 + P3 + ... + Pn. This is your starting point!
  2. Convert Units: Ensure all values are in consistent units. Pressure should typically be in atm, torr, or Pa, and temperature should be in Kelvin.
  3. Use Mole Fractions: When given the number of moles of each gas, use mole fractions to find partial pressures. The formula is Pi = Xi * Ptotal, where Pi is the partial pressure of gas i and Xi is its mole fraction.
  4. Ideal Gas Law: Remember the ideal gas law, PV = nRT, which is often needed to find the number of moles or partial pressures when other information is given.
  5. Check Your Work: After solving a problem, double-check your calculations and ensure that the sum of the partial pressures equals the total pressure.
  6. Be Careful with Molar Masses: Always use the correct molar masses for each gas when converting between mass and moles. A mistake here can throw off your entire calculation!
  7. Practice Regularly: The more you practice, the more comfortable you'll become with these types of problems. Consistency is key!

Conclusion

Dalton's Law is a straightforward concept once you grasp the basics and practice applying it. By understanding the relationships between partial pressures, mole fractions, and total pressure, you can confidently tackle a wide range of problems. Remember to convert units, use the ideal gas law when necessary, and always double-check your work. With these tips and plenty of practice, you'll be solving Dalton's Law problems like a pro in no time! Keep practicing, and you'll nail it. Good luck, and happy studying!