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Related Concept Videos

Buffers02:56

Buffers

176.5K
A solution containing appreciable amounts of a weak conjugate acid-base pair is called a buffer solution, or a buffer. Buffer solutions resist a change in pH when small amounts of a strong acid or a strong base are added. A solution of acetic acid and sodium acetate is an example of a buffer that consists of a weak acid and its salt: CH3COOH (aq) + CH3COONa (aq). An example of a buffer that consists of a weak base and its salt is a solution of ammonia and ammonium chloride: NH3 (aq) + NH4Cl...
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Calculating pH Changes in a Buffer Solution02:45

Calculating pH Changes in a Buffer Solution

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A buffer can prevent a sudden drop or increase in the pH of a solution after the addition of a strong acid or base up to its buffering capacity; however, such addition of a strong acid or base does result in the slight pH change of the solution. The small pH change can be calculated by determining the resulting change in the concentration of buffer components, i.e., a weak acid and its conjugate base or vice versa. The concentrations obtained using these stoichiometric calculations can be used...
60.1K
Chemical Equilibria: Systematic Approach to Equilibrium Calculations01:21

Chemical Equilibria: Systematic Approach to Equilibrium Calculations

1.8K
Equilibrium calculations for systems involving multiple equilibria are often complex. For example, to calculate the solubility of a sparingly soluble salt in an aqueous solution in the presence of a common ion, one must consider all the equilibria in this solution. Calculations for these systems can be complicated and tedious, so a systematic approach with a series of steps is often helpful. The process is detailed below.
The first step is to identify all the chemical reactions involved, The...
1.8K
Buffer Effectiveness02:19

Buffer Effectiveness

57.5K
Buffer solutions do not have an unlimited capacity to keep the pH relatively constant . Instead, the ability of a buffer solution to resist changes in pH relies on the presence of appreciable amounts of its conjugate weak acid-base pair. When enough strong acid or base is added to substantially lower the concentration of either member of the buffer pair, the buffering action within the solution is compromised.
The buffer capacity is the amount of acid or base that can be added to a given volume...
57.5K
Weak Base Solutions03:21

Weak Base Solutions

26.4K
Some compounds produce hydroxide ions when dissolved by chemically reacting with water molecules. In all cases, these compounds react only partially and so are classified as weak bases. These types of compounds are also abundant in nature and important commodities in various technologies. For example, global production of the weak base ammonia is typically well over 100 metric tons annually, being widely used as an agricultural fertilizer, a raw material for chemical synthesis of other...
26.4K
Buffers: Overview01:30

Buffers: Overview

10.9K
Buffers play a crucial role in stabilizing the pH of a solution by mitigating the effects of small amounts of added acid or base. They consist of a weak acid and its conjugate base or a weak base and its conjugate acid. A solution of acetic acid and sodium acetate is an example of a buffer that consists of a weak acid and its salt: CH3COOH (aq) + CH3COONa (aq). An example of a buffer that consists of a weak base and its salt is a solution of ammonia and ammonium chloride: NH3 (aq) + NH4Cl (aq).
10.9K

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Related Experiment Video

Updated: Mar 13, 2026

Multiscale Sampling of a Heterogeneous Water/Metal Catalyst Interface using Density Functional Theory and Force-Field Molecular Dynamics
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Multiscale Sampling of a Heterogeneous Water/Metal Catalyst Interface using Density Functional Theory and Force-Field Molecular Dynamics

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ACCURATE CHEMICAL MASTER EQUATION SOLUTION USING MULTI-FINITE BUFFERS.

Youfang Cao1, Anna Terebus1, Jie Liang1

  • 1Department of Bioengineering, University of Illinois at Chicago, Chicago, IL, USA.

Multiscale Modeling & Simulation : a SIAM Interdisciplinary Journal
|October 21, 2016
PubMed
Summary

The Accurate CME (ACME) algorithm effectively reduces state space for discrete chemical master equations (dCMEs). This enables accurate computation of probability landscapes and rare event probabilities in complex biological networks.

Keywords:
chemical master equationfirst passage time distributionstate space truncationsteady state probability landscapestochastic biological networkstime-evolving probability landscapes

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Area of Science:

  • Computational Biology
  • Chemical Kinetics
  • Systems Biology

Background:

  • The discrete chemical master equation (dCME) is crucial for studying stochasticity in mesoscopic networks.
  • Solving dCMEs is challenging due to large state spaces in multi-scale networks with disparate reaction rates.

Purpose of the Study:

  • To introduce an algorithm for accurate and efficient solutions to dCMEs.
  • To enable computation of probability landscapes and rare event probabilities.

Main Methods:

  • The Accurate CME (ACME) algorithm uses multi-finite buffers to reduce state space.
  • A theoretical framework aggregates microstates into macrostates using independent birth and death processes.
  • A priori methods determine truncation errors and buffer sizes for a given error tolerance.

Main Results:

  • ACME computes exact steady-state and time-evolving probability landscapes for multi-scale networks.
  • Successfully computed landscapes for toggle switch, phage-lambda, and MAPK cascade networks.
  • Enabled computation of rare event probabilities from first-passage times.

Conclusions:

  • The ACME method provides accurate and efficient solutions for dCMEs in a wide range of networks.
  • Addresses limitations of simulation-based techniques for problems with large time-scale separations.