# Calculating equivalent mass

Defining the equivalent of a substance

The equiv­a­lent of a sub­stance, also known as the equiv­a­lent quan­ti­ty of a sub­stance, refers to the quan­ti­ty of a sub­stance that in­ter­acts with one mole of hy­dro­gen ions (in an acid–base re­ac­tion) or elec­trons (in a re­dox re­ac­tion). Equiv­a­lent mass­es are nec­es­sary to en­sure cor­rect cal­cu­la­tions for chem­i­cal re­ac­tions be­tween sub­stances. Us­ing equiv­a­lents, we can ob­tain a cor­rect val­ue with­out long re­ac­tion for­mu­las, be­cause we only have to know that the chem­i­cal sub­stances in­ter­act, or that the sub­stance is the prod­uct of a chem­i­cal re­ac­tion.

To start, let’s talk about what an equiv­a­lent of a sub­stance is. Ac­cord­ing to the clas­si­cal def­i­ni­tion, an equiv­a­lent of a sub­stance is a con­di­tion­al or real par­ti­cle that can be equiv­a­lent in any way to a cation of hy­dro­gen in ion ex­change and acid-base re­ac­tions, or to an elec­tron in re­dox re­ac­tions.

Any sub­stance has sev­er­al defin­ing char­ac­ter­is­tics, and its equiv­a­lent mass, in­di­cat­ed as M equ, is one of the most im­por­tant of all. The mo­lar mass of a sub­stance is easy to de­ter­mine: sim­ply add up the mo­lar mass­es of the atoms in the sub­stance’s chem­i­cal for­mu­la.

The mo­lar mass of a sub­stance is just one of sev­er­al pa­ram­e­ters need­ed to cor­rect­ly cal­cu­late equiv­a­lence.

Some guide­lines for find­ing the equiv­a­lent of a sub­stance

The for­mu­la for de­ter­min­ing a sub­stance’s equiv­a­lent mass de­pends on the class of the com­pound in ques­tion. It is easy to find the equiv­a­lent mass for ox­ides, for ex­am­ple: di­vide the mo­lar mass of the com­pound by the va­lence of the non-oxy­gen el­e­ment mul­ti­plied by its num­ber of atoms. Let’s look at the equiv­a­lent mass for gold(III) ox­ide, with the for­mu­la Au₂O₃.

Us­ing sim­ple cal­cu­la­tions, we get:

(197x2+16x3)/3x2= 73.7 g/mol.

To cal­cu­late the equiv­a­lent mass of a base, sim­ply di­vide the mo­lar mass of the base by the num­ber of hy­drox­yl groups. Take, for ex­am­ple, cal­ci­um hy­drox­ide Ca(OH)₂. A few sim­ple cal­cu­la­tions yield an equiv­a­lent of 37g/mol.

To find the equiv­a­lent of an acid, di­vide the acid’s mo­lar mass by the num­ber of pro­tons. Here is a sim­ple ex­am­ple us­ing sul­fu­ric acid:

(1x2+32x1+16x4)/2 = 49 g/mol.

Find­ing the equiv­a­lent of a salt is also sim­ple: mul­ti­ply the num­ber of met­al atoms by their ox­i­da­tion state, then di­vide its mo­lar mass by the re­sult. Click here to learn about some safe chem­i­cal ex­per­i­ments that dive deep­er into this ques­tion.

## Ex­per­i­ments to find the equiv­a­lent mass of a sub­stance

This ex­per­i­ment is quite in­ter­est­ing, and can be used to demon­strate how to cal­cu­late the equiv­a­lent mass of a sub­stance. But it must be per­formed with ex­treme cau­tion: be­fore per­form­ing any ex­per­i­ment, al­ways read the nec­es­sary sci­en­tif­ic lit­er­a­ture and tech­niques of con­duct­ing ex­per­i­ments.

Warn­ing! Don’t try to con­duct this ex­per­i­ment with­out pro­fes­sion­al su­per­vi­sion!

You’ll need:

• test tube;
• bu­rette;
• fun­nel;
• corks;
• tubes;
• cal­cu­la­tor;
• the Pe­ri­od­ic Ta­ble;
• hy­drochlo­ric acid;
• zinc plates;
• barom­e­ter;
• ther­mome­ter;
• gloves;
• chem­i­cal res­pi­ra­tor;
• pro­tec­tive glass­es.

Re­mem­ber that this so­lu­tion can­not be pre­pared at home. Hy­drochlo­ric acid is dan­ger­ous: it caus­es se­vere burns if it comes into con­tact with the skin. Wear gloves when con­duct­ing the ex­per­i­ment. Also use a chem­i­cal res­pi­ra­tor and pro­tec­tive glass­es, as hy­drochlo­ric acid fumes are harm­ful to the res­pi­ra­to­ry sys­tem and eyes.

If any acid ac­ci­den­tal­ly touch­es the skin, rinse the af­fect­ed area with run­ning wa­ter and use bak­ing soda to neu­tral­ize the acid.

This method is based on mea­sur­ing the vol­ume of hy­dro­gen re­leased as the re­sult of a re­ac­tion be­tween a met­al and an acid. The equiv­a­lent of zinc is de­ter­mined us­ing a bu­rette con­nect­ed via tub­ing to a fun­nel and a test tube. The ap­pa­ra­tus func­tions as a sys­tem of com­mu­ni­cat­ing ves­sels.

Fill the bu­rette with wa­ter. Use the pipette to trans­fer a few milliliters of hy­drochlo­ric acid to the bot­tom of the test tube. Tilt the test tube and in­sert the piece of zinc, tak­ing care not to let it touch the acid. Ad­just the height of the fun­nel to bring the wa­ter lev­el in the bu­rette to “0”. Cork the test tube and knock the zinc into the acid. You will ob­serve a no­tice­able re­lease of hy­dro­gen gas, which will force some of the wa­ter out of the bu­rette. Note the dif­fer­ence in ini­tial and fi­nal wa­ter lev­els in the bu­rette to mea­sure how much gas was re­leased. Tak­ing into ac­count the tem­per­a­ture in the lab­o­ra­to­ry, at­mo­spher­ic pres­sure, and the pres­sure of the wa­ter va­por in the bu­rette, you can cal­cu­late the equiv­a­lent mass of the met­al us­ing the cor­rect for­mu­la with rea­son­able ac­cu­ra­cy. In­ci­den­tal­ly, if you are in­ter­est­ed in how wa­ter’s tem­per­a­ture can be in­flu­enced by dis­solv­ing sub­stances in it, you can give this ex­per­i­ment a try.