Calculating Equilibrium Concentrations · 计算平衡浓度
| English | 中文 | Pinyin · 拼音 |
|---|---|---|
| approximation/əˌprɒksɪˈmeɪʃn/ | 近似 | jìn sì |
Solving for the unknown amounts
- Given the starting amounts and $K$, can you predict the end?
- Yes -- set up a table with an unknown change "$x$."
- Solve the equation $K$ gives you for $x$.
- Then read off exactly how much of each is present.
求解未知的量
- 给定起始量和 $K$,你能预测终态吗?
- 能——建一张表,把未知的变化写成"$x$"。
- 解 $K$ 给你的方程,求出 $x$。
- 然后读出每种物质到底有多少。
Let the change be x
- Build an ICE table with the change written as $x$.
- Reactants lose $x$; products gain $x$, each times its coefficient.
- The equilibrium row is written in terms of $x$.
把变化设为 x
- 建一张三段式表,把变化写成 $x$。
- 反应物减少 $x$;产物增加 $x$,各乘以它的系数。
- 平衡那一行用 $x$ 表示。
In an ICE table, a reactant's equilibrium amount is written as... · 在ICE表中，反应物的平衡量写作...
Reactants are used up, so their amount is (initial $- x$). · 反应物被消耗，因此其量为(初始$- x$)。
In an ICE table, a product's equilibrium amount is written as initial plus . · 在ICE表中，产物的平衡量写作初始值加上。
Products are formed, so their amount is (initial $+ x$). · 产物生成，因此其量为(初始$+ x$)。
Solve the K equation
- Put the equilibrium row into the $K$ expression.
- Set it equal to the known $K$ and solve for $x$.
- Then plug $x$ back to get each concentration.
解 K 方程
- 把平衡那一行代入 $K$ 表达式。
- 令它等于已知的 $K$,解出 $x$。
- 然后把 $x$ 代回,得到每个浓度。
To find $x$, you set the $K$ expression equal to... · 要求解$x$，需将$K$表达式等于...
Set the expression equal to $K$ and solve for $x$. · 将表达式等于$K$并求解$x$。
A handy approximation
- When $K$ is very small, $x$ is tiny compared to the start.
- You can often use this approximation 近似 and ignore $x$ in "$(\text{start} - x)$."
- This avoids the quadratic and still gives a good answer.
一个方便的近似
- 当 $K$ 很小时,$x$ 与起始量相比很微小。
- 你常可以用这个近似,在 "$(\text{start} - x)$" 中忽略 $x$。
- 这避免了二次方程,仍给出不错的答案。
Solve for equilibrium amounts · 求解平衡量
Use x to find the equilibrium concentrations from K. · 使用x从K求出平衡浓度。
When $K$ is very small, you can often ignore $x$ in (initial $- x$). · 当 $K$ 非常小时，通常可以忽略 $x$ 在（初始 $- x$).
A small $K$ makes $x$ negligible compared to the start. · 小的 $K$ 使得 $x$ 与起始值相比可忽略不计。
Start with $1.0\ \text{M}$ reactant and a small $K$. If $x$ is tiny, what is the reactant concentration?
- $(1.0 - x) \approx 1.0$ when $x$ is negligible.
- So the reactant stays close to $1.0\ \text{M}$.
从 $1.0\ \text{M}$ 反应物和小的 $K$ 开始。若 $x$ 很微小,反应物浓度是多少?
- 当 $x$ 可忽略时,$(1.0 - x) \approx 1.0$。
- 所以反应物保持接近 $1.0\ \text{M}$。
The "ignore $x$" approximation should be checked by confirming $x$ is under about... · “忽略$x$”近似应通过确认$x$低于约...来检验。
If $x$ exceeds about 5%, solve the full quadratic instead. · 若$x$超过约5%，则求解完整二次方程。
A solution for $x$ that gives a negative concentration should be rejected. · 给出负浓度的$x$解应被舍去。
Concentrations cannot be negative, so that root is unphysical. · 浓度不能为负，因此该根不符合物理实际。
The "ignore $x$" shortcut is valid only when $K$ is small (so $x$ is much less than the starting amount) -- check that $x$ is under about 5% of the start, or solve the full quadratic. Set the ICE signs correctly: reactants minus $x$, products plus $x$. And confirm $x$ is physically reasonable (no negative concentrations).
"忽略 $x$" 的捷径只在 $K$ 很小(使 $x$ 远小于起始量)时有效——检查 $x$ 是否小于起始量的约 5%,否则解完整的二次方程。把三段式的符号设对:反应物减 $x$,产物加 $x$。而且要确认 $x$ 在物理上合理(没有负浓度)。
To find equilibrium concentrations, write the change as $x$ in an ICE table, put the equilibrium row into the $K$ expression, and solve for $x$. When $K$ is small, an approximation ($x$ negligible) avoids the quadratic -- but only if $x$ stays under about 5% of the start.
要求平衡浓度,在三段式表中把变化写成 $x$,把平衡那一行代入 $K$ 表达式,解出 $x$。当 $K$ 很小时,一个近似($x$ 可忽略)避免了二次方程——但仅当 $x$ 保持在起始量的约 5% 以下时。