Contoh Soal Hukum Dalton Dan Pembahasannya

Oct 30, 2025 by Jhon Lennon 43 views

Alright, guys, let's dive into the fascinating world of Dalton's Law! If you're scratching your head over partial pressures and gas mixtures, you've come to the right place. This article is packed with example problems and step-by-step solutions to help you master this essential concept in chemistry. Trust me, once you get the hang of it, you'll be solving these problems like a pro!

What is Dalton's Law?

Before we jump into the problems, let's do a quick recap of what Dalton's Law actually states. Dalton's Law of Partial Pressures basically says that the total pressure exerted by a mixture of gases is equal to the sum of the partial pressures of each individual gas. In simpler terms, each gas in the mixture contributes to the overall pressure as if it were the only gas present. Think of it like a group project where everyone's effort adds up to the final result. Mathematically, it’s expressed as:

P_total = P₁ + P₂ + P₃ + ... + P_n

Where:

P_total is the total pressure of the gas mixture
P₁, P₂, P₃, ..., P_n are the partial pressures of each individual gas

Understanding this simple formula is the key to tackling Dalton's Law problems. Now, let's get our hands dirty with some examples!

Example Problems and Solutions

Problem 1: Mixing Gases

Problem: A container holds 2.0 L of nitrogen gas at a pressure of 3.0 atm and 3.0 L of oxygen gas at a pressure of 4.0 atm. If these two gases are mixed into a 5.0 L container, what is the total pressure of the mixture?

Solution:

Okay, let's break this down step by step. First, we need to find the partial pressure of each gas after it's been transferred to the new container. We'll use Boyle's Law (P₁V₁ = P₂V₂) for this.

For Nitrogen (N₂):

P₁ = 3.0 atm
V₁ = 2.0 L
V₂ = 5.0 L
P₂ = ?

Using Boyle's Law:

0 atm * 2.0 L = P₂ * 5.0 L
0 atm = P₂ * 5.0 L

P₂ = (3.0 atm * 2.0 L) / 5.0 L = 1.2 atm

So, the partial pressure of nitrogen in the mixture is 1.2 atm.

For Oxygen (O₂):

P₁ = 4.0 atm
V₁ = 3.0 L
V₂ = 5.0 L
P₂ = ?

Using Boyle's Law:

0 atm * 3.0 L = P₂ * 5.0 L
0 atm = P₂ * 5.0 L

P₂ = (4.0 atm * 3.0 L) / 5.0 L = 2.4 atm

So, the partial pressure of oxygen in the mixture is 2.4 atm.

Now, we can use Dalton's Law to find the total pressure:

P_total = P_N2 + P_O2 = 1.2 atm + 2.4 atm = 3.6 atm

Answer: The total pressure of the gas mixture is 3.6 atm.

Problem 2: Collecting Gas Over Water

Problem: Hydrogen gas is collected over water at 22°C. The total pressure of the collected gas is 758 torr. The vapor pressure of water at 22°C is 20 torr. What is the partial pressure of the hydrogen gas?

Solution:

When a gas is collected over water, the collected gas is actually a mixture of the gas you're interested in (in this case, hydrogen) and water vapor. The total pressure is the sum of the partial pressure of the hydrogen gas and the vapor pressure of water.

Dalton's Law helps us here:

P_total = P_H2 + P_H2O

We know:

P_total = 758 torr
P_H2O = 20 torr

We want to find P_H2.

Rearranging the equation:

P_H2 = P_total - P_H2O = 758 torr - 20 torr = 738 torr

Answer: The partial pressure of the hydrogen gas is 738 torr.

Problem 3: Mole Fractions and Partial Pressures

Problem: A gas mixture contains 4.0 grams of helium (He) and 16.0 grams of oxygen (O₂) in a 10.0 L container at 300 K. Calculate the partial pressure of each gas and the total pressure.

Solution:

This problem involves mole fractions, which are related to partial pressures. The mole fraction of a gas in a mixture is the ratio of the number of moles of that gas to the total number of moles of all gases in the mixture.

Step 1: Calculate the number of moles of each gas.

Moles of He = mass / molar mass = 4.0 g / 4.0 g/mol = 1.0 mol
Moles of O₂ = mass / molar mass = 16.0 g / 32.0 g/mol = 0.5 mol

Step 2: Calculate the total number of moles.

Total moles = moles of He + moles of O₂ = 1.0 mol + 0.5 mol = 1.5 mol

Step 3: Calculate the mole fraction of each gas.

Mole fraction of He = moles of He / total moles = 1.0 mol / 1.5 mol = 0.67
Mole fraction of O₂ = moles of O₂ / total moles = 0.5 mol / 1.5 mol = 0.33

Step 4: Use the Ideal Gas Law to find the total pressure.

The Ideal Gas Law is PV = nRT, where:

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

We can rearrange this to solve for P: P = nRT / V

P_total = (1.5 mol * 0.0821 L atm / (mol K) * 300 K) / 10.0 L = 3.69 atm

Step 5: Calculate the partial pressure of each gas.

The partial pressure of a gas is equal to its mole fraction multiplied by the total pressure.

P_He = mole fraction of He * P_total = 0.67 * 3.69 atm = 2.47 atm
P_O2 = mole fraction of O₂ * P_total = 0.33 * 3.69 atm = 1.22 atm

Answer:

Partial pressure of helium = 2.47 atm
Partial pressure of oxygen = 1.22 atm
Total pressure = 3.69 atm

Key Takeaways and Tips

Dalton's Law is all about partial pressures adding up! Always remember the core principle: the total pressure of a gas mixture equals the sum of the partial pressures of each gas.
Boyle's Law is your friend. When dealing with changes in volume and pressure, Boyle's Law (P₁V₁ = P₂V₂) is often essential for finding the new partial pressures.
Don't forget about water vapor. When collecting gases over water, remember to subtract the vapor pressure of water to get the true partial pressure of the gas.
Mole fractions are powerful. When you have the masses of the gases, convert them to moles, calculate mole fractions, and use those to find partial pressures.
Practice, practice, practice! The more problems you solve, the more comfortable you'll become with applying Dalton's Law.

Conclusion

So, there you have it! A comprehensive guide to solving Dalton's Law problems. Remember to take it slow, break down each problem into smaller steps, and don't be afraid to ask for help if you get stuck. With a little practice, you'll be a Dalton's Law master in no time. Keep up the great work, and happy problem-solving!

Now you should have a solid foundation for tackling various Dalton's Law problems. Good luck with your studies! Remember, understanding the concepts is key, and practice makes perfect. Don't hesitate to revisit these examples and try similar problems on your own. Chemistry can be challenging, but with the right approach and a bit of effort, you can conquer any problem that comes your way!

If you found this guide helpful, feel free to share it with your friends and classmates. And don't forget to explore other chemistry topics to expand your knowledge. Happy learning!