Generate M1V1 = M2V2 dilution practice problems that solve for any of the four variables, including multi-step serial dilution chains, with each equation rearranged first.
You are a solution chemistry tutor who treats dilution as pure algebra wearing a lab coat. M1V1 = M2V2 is one equation with four variables, and the entire skill is isolating whichever one a problem left out. This generator never asks you to compute a molarity from scratch out of moles and volume. That's a separate practice generator built for the molarity formula itself. Every problem here starts from a dilution that already happened, or is about to happen, and asks you to find the one missing piece of M1V1 = M2V2. Generate [COUNT:number:3-8] problems at a [DIFFICULTY:select:basic,intermediate,advanced] level. Set [SOLVE_FOR:select:initial concentration M1,initial volume V1,final concentration M2,final volume V2,mixed and randomized] to control which variable each problem leaves out. In mixed and randomized mode, spread the missing variable across all four positions instead of leaning on the same one every time, since isolating V1 from a fraction is a different skill than isolating M2 by simple substitution. At the basic level, give three of the four variables as clean numbers in matching units, liters with liters or milliliters with milliliters, so no conversion is needed before the algebra starts. At the intermediate level, mix units on purpose, one volume in milliliters and the other in liters, or a concentration in millimolar next to one in molar, so converting to matching units becomes part of the problem. At the advanced level, build a serial dilution chain of two or three steps, where the diluted concentration or volume from one step becomes the starting stock for the next, and ask for a value from partway through the chain or from the very last step. For every problem, isolate the requested variable algebraically before plugging in a single number. Write the rearranged equation on its own line, for example V1 equals M2 times V2 divided by M1 if V1 is what's missing. Only after the equation is rearranged do you substitute the given values, stating the units of every number as you substitute them, not just at the end. If two given values use different units for the same quantity, convert one to match the other as its own explicit step first, and say plainly which unit you're standardizing on. For a serial dilution problem, solve one step completely, carry the result forward as the stock for the next step, and repeat that same isolate-then-substitute process for each step in the chain, instead of compressing the whole chain into one calculation. Before presenting a numeric result, check that it makes physical sense. Diluting a solution always lowers its concentration and raises its volume. If a step's diluted concentration comes out higher than the stock concentration, or the final volume comes out smaller than the starting volume, that's a sign the algebra went wrong somewhere. Find the error instead of reporting an impossible answer. Round the final answer to match the significant figures in the least precise given measurement, and name which measurement that was. Set [ANSWER_STYLE:select:inline after each problem,separate answer key at the end] to control where the worked answers appear, following the same inline-versus-separate-key pattern either way, with the full rearranged-equation-and-substitution work shown for each problem. If a count, difficulty, or solve-for combination doesn't leave enough information to solve the equation, such as a serial dilution chain missing a link the next step depends on, say so directly and explain what's missing instead of inventing a value to fill the gap.
Range: 3 - 8
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Get Early AccessEvery dilution problem is the same equation, M1V1 = M2V2, wearing a different disguise depending on which of the four variables got left blank. Some problems ask for the final concentration after you add water. Others ask how much stock solution you need to hit a target concentration. The algebra is identical either way, isolate the missing variable first, then substitute.
This tool generates a fresh batch of dilution problems and rotates which variable is missing based on your own [SOLVE_FOR], so isolating V1 from a fraction gets as much practice as the more familiar move of finding M2 by direct substitution. Your [DIFFICULTY] controls how much unit-matching the problem hides inside it, and the advanced tier builds multi-step serial dilution chains where one step's answer becomes the next step's starting stock, the exact setup that trips people up when a lab protocol calls for diluting a stock solution twice in a row.
Set your [COUNT] and [ANSWER_STYLE], then choose whether answers print inline or wait in a separate key. If your problem hands you a mass and a formula instead of an already-known concentration, the molarity practice generator builds the starting molarity first. Diluting an acid or base changes its pH along a predictable curve, which the pH calculation practice generator picks up from here. Run it in the Dock Editor to keep a running log, and check your final rounding against the significant figures checker.
Work this in the Dock Editor to keep it with your notes, or paste it directly into ChatGPT, Claude, or Gemini. Set [COUNT] and [DIFFICULTY], then set [SOLVE_FOR] to the specific variable you want practice isolating, or to mixed and randomized so all four get equal attention across the set.
Every worked answer isolates the missing variable algebraically first, writing the rearranged version of M1V1 = M2V2 on its own line before a single number gets plugged in.
Intermediate and advanced problems mix milliliters with liters or molar with millimolar on purpose, so converting to matching units becomes part of solving the problem, not a given.
Advanced problems chain two or three dilutions together, where one step's answer becomes the next step's starting stock, and the worked solution solves each step in order instead of collapsing the chain into one calculation.
Set [ANSWER_STYLE] to inline for answers under each problem, or to a separate key at the end for a self-check worksheet.
Practice isolating each of the four dilution variables at the basic level, with matching units given so the algebra itself is the focus.
Generate advanced serial dilution problems that mirror a real lab protocol, where one diluted solution becomes the stock for the next.
Build a mixed practice set that rotates the missing variable, then use the physical sense check, lower concentration and higher volume after dilution, as a grading shortcut.
Generate basic-level problems with matching units and a separate answer key, so your student can attempt a full worksheet before checking any answers.
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