🧪 溶液稀释计算器（C₁V₁ = C₂V₂）Solution Dilution Calculator (C₁V₁ = C₂V₂)

使用说明与常见问题How-to & FAQ

「溶液稀释计算器（C₁V₁ = C₂V₂）」是什么？What is the Solution Dilution Calculator (C₁V₁ = C₂V₂) tool?

按 C₁V₁ = C₂V₂ 求最终体积、最终浓度、所需原液体积或原液浓度中的任意一个，并给出稀释倍数和需要加入的溶剂量。浓度和体积的单位只要两边一致即可。本地处理。Solve C₁V₁ = C₂V₂ for the final volume, final concentration, stock volume or stock concentration, with the dilution factor and how much solvent to add. Any units work as long as both sides use the same ones. Processed locally.

如何使用「溶液稀释计算器（C₁V₁ = C₂V₂）」？How do I use the Solution Dilution Calculator (C₁V₁ = C₂V₂) tool?

在「溶液稀释计算器（C₁V₁ = C₂V₂）」中，填写「求」、「原液浓度 C₁」、「原液体积 V₁」、「最终浓度 C₂」、「最终体积 V₂」等参数，结果会随输入实时计算并显示在下方。In the Solution Dilution Calculator (C₁V₁ = C₂V₂): Fill in "Solve for", "Stock concentration C₁", "Stock volume V₁", "Final concentration C₂", "Final volume V₂"; results are recalculated instantly as you type.

C₁V₁ = C₂V₂ 是什么意思？What does C₁V₁ = C₂V₂ mean?

稀释时溶质的量不变，只是体积变大，所以原液浓度 × 原液体积 = 稀释后浓度 × 稀释后体积。例如要用 1 M 原液配 100 mL 0.1 M 溶液，需要 10 mL 原液，再加溶剂到 100 mL。Diluting keeps the amount of solute the same while the volume grows, so stock concentration × stock volume = final concentration × final volume. To make 100 mL of 0.1 M from a 1 M stock you need 10 mL of stock, topped up with solvent to 100 mL.

单位怎么选？Which units should I use?

任何单位都可以（mol/L、mg/mL、% 等，mL、L 等），只要两种浓度用同一单位、两种体积用同一单位。结果的单位和输入相同。Any units (mol/L, mg/mL, %, mL, L…) as long as both concentrations share one unit and both volumes share one unit. The answer comes out in the same units.

加入的溶剂为什么是“约”？Why is the solvent amount approximate?

V₂ − V₁ 只是近似值：有些溶液混合后体积不严格相加（如乙醇和水）。准确做法是把原液放进容量瓶，再加溶剂到刻度线。V₂ − V₁ is only approximate because some liquids do not add up exactly when mixed (ethanol and water, for example). The accurate way is to put the stock in a volumetric flask and fill to the mark.

能举个计算实例吗？Can you show a worked example?

例如在「溶液稀释计算器（C₁V₁ = C₂V₂）」中填 求 = 最终体积 V₂，原液浓度 C₁ = 1，原液体积 V₁ = 1，最终浓度 C₂ = 0.5，结果区显示：最终体积 V₂：2；稀释倍数 C₁/C₂：2×；操作：取 1 原液，加溶剂到总体积 2（约加入 1）；ℹ C₁V₁ = C₂V₂；体积单位和浓度单位两边要一致For example, entering Solve for = Final volume V₂, Stock concentration C₁ = 1, Stock volume V₁ = 1, Final concentration C₂ = 0.5 in the Solution Dilution Calculator (C₁V₁ = C₂V₂) gives: Final volume V₂: 2; Dilution factor C₁/C₂: 2×; How to make it: take 1 of stock and add solvent up to a total of 2 (about 1 added); ℹ C₁V₁ = C₂V₂; use the same volume unit and the same concentration unit on both sides

哪些输入会被检查？Which inputs are validated?

「溶液稀释计算器（C₁V₁ = C₂V₂）」会检查这些输入——「原液浓度 C₁」、「最终浓度 C₂」：可留空；「原液体积 V₁」：须大于 0；「最终体积 V₂」：须大于 0；绝对值超过 10¹⁵ 的数也会被拒绝。不符合时结果区显示具体提示，不会给出数字。The Solution Dilution Calculator (C₁V₁ = C₂V₂) checks its inputs — "Stock concentration C₁", "Final concentration C₂": optional; "Stock volume V₁": must be greater than 0; "Final volume V₂": must be greater than 0; numbers above 10¹⁵ in absolute value are rejected too. When a value fails, the result area names the problem instead of showing a number.

有哪些选项可以调整？What options can I adjust?

「溶液稀释计算器（C₁V₁ = C₂V₂）」的设置：「求」可选 所需原液体积 V₁、最终体积 V₂、最终浓度 C₂、原液浓度 C₁（默认 所需原液体积 V₁）；「原液浓度 C₁」默认 1；「原液体积 V₁」默认 10；「最终浓度 C₂」默认 0.1；「最终体积 V₂」默认 100。每次生成结果都按当前设置处理。Settings in the Solution Dilution Calculator (C₁V₁ = C₂V₂) — "Solve for": Stock volume V₁, Final volume V₂, Final concentration C₂, Stock concentration C₁ (default Stock volume V₁); "Stock concentration C₁" default 1; "Stock volume V₁" default 10; "Final concentration C₂" default 0.1; "Final volume V₂" default 100. The result always uses the current settings.

计算结果可以用于作业或工程吗？Can I use the results for homework or engineering?

「溶液稀释计算器（C₁V₁ = C₂V₂）」使用教科书标准公式（公式写在说明和常见问题中），适合学习和估算核对；涉及安全的工程设计请以规范和实测为准。The Solution Dilution Calculator (C₁V₁ = C₂V₂) uses standard textbook formulas (given in the description and FAQ), which is good for learning and checking estimates; for safety-critical engineering follow codes and measured values.

「溶液稀释计算器（C₁V₁ = C₂V₂）」免费吗？需要注册吗？Is the Solution Dilution Calculator (C₁V₁ = C₂V₂) free? Do I need an account?

「溶液稀释计算器（C₁V₁ = C₂V₂）」完全免费，无需注册或安装，打开网页即可使用，手机和电脑都能用；输入的内容只在你的浏览器本地处理。The Solution Dilution Calculator (C₁V₁ = C₂V₂) is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.