Calculating Hydroxide Ion Concentration In Ammonia Solution PH 11.8

Hey there, chemistry enthusiasts! Today, we're diving into a fascinating problem involving ammonia and its pH, and trust me, it's not as daunting as it sounds. We're going to figure out the concentration of hydroxide ions ($[OH^{-}]$) in an ammonia solution with a pH of 11.8. Don't worry, we'll break it down step by step and make it super easy to follow. So, grab your lab coats (figuratively, of course!) and let's get started!

Understanding pH, pOH, and Ion Concentrations

Before we jump into the calculations, let's quickly recap some key concepts. These are the building blocks we'll use to solve our problem. Think of them as the essential tools in our chemistry toolkit. First off, pH is a measure of how acidic or basic a solution is. It ranges from 0 to 14, where 7 is neutral, values below 7 are acidic, and values above 7 are basic (or alkaline). Now, pOH is like the flip side of pH. It measures the concentration of hydroxide ions ($[OH^{-}]$) in a solution. The cool thing is that pH and pOH are related! They always add up to 14 at 25°C. This relationship is super handy because if we know the pH, we can easily find the pOH, and vice versa.

Next up, we have ion concentrations. These tell us how much of a particular ion is dissolved in a solution. We often express these concentrations in moles per liter (mol/L), which is also known as molarity (M). In our case, we're interested in two ions the hydronium ion ($[H_3O^{+}]$) and the hydroxide ion ($[OH^{-}]$). These ions are like the yin and yang of aqueous solutions. Their concentrations are inversely related. When one goes up, the other goes down. And here's a crucial relationship the product of $[H_3O^{+}]$ and $[OH^{-}]$ is always equal to $1.0 imes 10^{-14}$ at 25°C. This is called the ion product of water ($K_w$) and it's a fundamental constant in aqueous chemistry. To make things even easier, we have some handy formulas to work with.

• $[H_3O^{+}] = 10^{-pH}$ This formula lets us calculate the hydronium ion concentration if we know the pH.
• $[OH^{-}] = 10^{-pOH}$ Similarly, this formula helps us find the hydroxide ion concentration if we know the pOH.
• $pH + pOH = 14$ This is the relationship we talked about earlier, connecting pH and pOH.
• $[H_3O^{+}][OH^{-}] = 10^{-14}$ This is the ion product of water, linking the concentrations of hydronium and hydroxide ions.

With these concepts and formulas in our arsenal, we're well-equipped to tackle our ammonia problem!

Step-by-Step Solution Calculating Hydroxide Ion Concentration

Okay, guys, let's get down to business and solve this problem step by step. Remember, our goal is to find the concentration of hydroxide ions ($[OH^{-}]$) in an ammonia solution with a pH of 11.8. So, let's put on our thinking caps and break it down. The first thing we need to do is figure out the pOH of the solution. Why? Because we have a formula that directly relates pOH to the hydroxide ion concentration. And guess what? We know the pH! We can use the relationship between pH and pOH to find our missing piece.

Remember the formula $pH + pOH = 14$? This is our golden ticket. We know the pH is 11.8, so we can plug that into the equation and solve for pOH. It looks like this: $11.8 + pOH = 14$. To isolate pOH, we simply subtract 11.8 from both sides of the equation. This gives us $pOH = 14 - 11.8 = 2.2$. Awesome! We've found the pOH of the solution. Now, let's move on to the next step. We've unlocked the pOH, and now it's time to use it to find the hydroxide ion concentration. Remember the formula $[OH^{-}] = 10^{-pOH}$? This is where that formula comes into play. We know the pOH is 2.2, so we can plug that into the formula. It looks like this: $[OH^{-}] = 10^{-2.2}$. Now, we just need to calculate this value. You can use a calculator for this, or if you're feeling ambitious, you can use logarithms. But let's stick with the calculator for now to keep things simple. When you plug $10^{-2.2}$ into your calculator, you should get approximately $6.31 imes 10^{-3}$.

This number represents the hydroxide ion concentration in moles per liter (mol/L). So, the concentration of $[OH^{-}]$ ions in the ammonia solution is approximately $6.31 imes 10^{-3} M$. We've done it! We've successfully calculated the hydroxide ion concentration using the pH and some handy formulas. Pat yourselves on the back, guys! Now, let's recap the steps we took to make sure we've got it all down.

1. We used the relationship $pH + pOH = 14$ to find the pOH of the solution.
2. We plugged the pOH value into the formula $[OH^{-}] = 10^{-pOH}$ to calculate the hydroxide ion concentration.

See? It wasn't so bad after all! Chemistry can be fun when we break it down into manageable steps. Now, let's move on and explore why this is important and what it tells us about the ammonia solution.

Why This Matters Understanding the Significance of $[OH^{-}]$

So, we've calculated the hydroxide ion concentration, but why does it even matter? What does this number tell us about the ammonia solution? Well, the hydroxide ion concentration is a key indicator of the solution's basicity. Remember, basic solutions have a higher concentration of hydroxide ions than hydronium ions. The higher the $[OH^{-}]$, the more basic the solution. In our case, we found that the hydroxide ion concentration is $6.31 imes 10^{-3} M$. This is a relatively high concentration, which confirms that our ammonia solution is indeed basic, as we already knew from its pH of 11.8. But it goes beyond just confirming what we already knew. The $[OH^{-}]$ value gives us a quantitative measure of the solution's basicity. It tells us exactly how much hydroxide ions are present in the solution, which can be crucial for many applications.

For example, in chemical reactions, the concentration of hydroxide ions can affect the reaction rate and the equilibrium position. In environmental chemistry, the $[OH^{-}]$ can influence the solubility of metals and the fate of pollutants. In biological systems, the pH and the hydroxide ion concentration play a vital role in enzyme activity and cellular processes. So, knowing the hydroxide ion concentration is not just an academic exercise. It has real-world implications in various fields. Now, let's think about ammonia specifically. Ammonia ($NH_3$) is a weak base. This means that it doesn't completely dissociate in water to form hydroxide ions. Instead, it reaches an equilibrium between the ammonia molecules, water molecules, ammonium ions ($NH_4^{+}$), and hydroxide ions ($OH^{-}$). The equilibrium lies on the side of the reactants, meaning that only a small fraction of the ammonia molecules react with water to form hydroxide ions. This is why ammonia solutions are considered weak bases, even though they can have a relatively high pH. The hydroxide ion concentration we calculated reflects this equilibrium. It tells us how much hydroxide ions are present in the solution at equilibrium, which is a balance between the forward reaction (ammonia reacting with water) and the reverse reaction (ammonium ions and hydroxide ions reacting to form ammonia and water). This equilibrium is described by the base dissociation constant ($K_b$), which is a measure of the strength of a base. The higher the $K_b$, the stronger the base. Ammonia has a $K_b$ value of $1.8 imes 10^{-5}$, which is relatively small, indicating that it is a weak base.

The hydroxide ion concentration is directly related to the $K_b$ value. By knowing the $[OH^{-}]$, we can actually calculate the $K_b$ or vice versa. This connection between hydroxide ion concentration and the equilibrium constant highlights the importance of understanding ion concentrations in chemical systems. So, to sum it up, the hydroxide ion concentration is not just a number. It's a window into the solution's basicity, its chemical behavior, and its role in various processes. It's a piece of the puzzle that helps us understand the bigger picture of chemistry. Now, let's wrap things up with a quick summary of what we've learned today.

Key Takeaways Mastering pH and Ion Calculations

Alright, guys, we've covered a lot of ground today! Let's take a moment to recap the key takeaways from our pH and ion concentration adventure. We started with a seemingly complex problem finding the hydroxide ion concentration in an ammonia solution with a pH of 11.8. But we broke it down into manageable steps and conquered it like chemistry champions! First, we refreshed our understanding of pH, pOH, and ion concentrations. We learned that pH is a measure of acidity or basicity, while pOH measures the hydroxide ion concentration. We also discovered the crucial relationship $pH + pOH = 14$ and the ion product of water, $[H_3O^{+}][OH^{-}] = 10^{-14}$. These are fundamental concepts that form the basis of acid-base chemistry.

Then, we tackled the problem head-on. We used the pH to calculate the pOH, and then we used the pOH to find the hydroxide ion concentration. We plugged the values into the appropriate formulas and arrived at our answer: $[OH^{-}] = 6.31 imes 10^{-3} M$. We saw how these formulas are powerful tools for solving chemistry problems. We also discussed why the hydroxide ion concentration is important. It's not just a random number it's a key indicator of a solution's basicity and its behavior in chemical reactions. We learned that a high $[OH^{-}]$ indicates a basic solution, and we explored how this relates to the equilibrium of weak bases like ammonia. Finally, we touched upon the real-world implications of hydroxide ion concentration in various fields, from chemical reactions to environmental chemistry and biological systems.

So, what's the big picture? Well, we've learned that pH and ion concentrations are not just abstract concepts they are essential for understanding the behavior of solutions and chemical systems. By mastering these concepts, we can unlock a deeper understanding of the world around us. Remember, chemistry is not just about memorizing formulas and equations. It's about understanding the underlying principles and applying them to solve problems. And that's exactly what we've done today! So, keep exploring, keep questioning, and keep learning. Chemistry is a fascinating journey, and there's always something new to discover. Thanks for joining me on this adventure, and I'll see you next time for more chemistry fun!

A. $6.31 imes 10^{-3}$