# reaction time

Two spherical pieces of calcium carbonate A and B are submerged in two beakers of hydrochloric acid of the same volume and the same concentration at room temperature. The mass of A is eight times of that of B. Hydrochloric acid is the limiting reactant in both cases. Which reaction ends first?

I'm sorry that there is a mistake.Hydrochloric acid is in excess in both cases.

The rate of reaction depends on the surface area of calcium carbonate.

Yet, a higher rate does not guarantee a shorter reaction time, because the reaction of case B involves a larger mass. 'More' reaction at a higher rate does not necessarily mean a short reaction time.

not case B, it's case A, I mixed them up...

### 3 個解答

• 最愛解答

sky, 雖然你很用心的洋洋灑灑寫了數百字,

我不得不告訴你, 那些幾乎都與問題無關, 而且答案簡單得不用考慮你列出的一堆公式.

rate of this reaction depends on:

- concentration of HCl

- surface area of calcium carbonate

concentration of HCl is kept for for both cases, so one needs not to consider this.

surface area... did you notice the mass ratio of A to B ?

8 times... very strange, right?

calcium carbonate has constant density while they are SPHEREs (balls).

- mass = volume x density

the volume of A is 8-times of that of B

- volume is proportional to cube of radius; volume = (4/3)*pi*r^3

radius ratio of A to B = 2:1

- surface area of sphere is proportional to square of radius; area = 4*pi*r^2

surface area ratio of A to B = 4:1

now it's obvious that A has larger surface area than B,

so reaction rate for A is higher than that of B;

reaction of A ends first.

說穿了, 勉強算是一道數學題吧.

主要是考核你, 有沒有仔細閱讀題目, 留意到"spherical", 然後將mass 與surface area 連繫起來.

大意的話, 恐怕就會像sky 浪費時間心機, 卻又答不對重點了.

2012-02-21 03:12:45 補充：

不用做實驗也能推斷出來.

2012-02-22 09:40:26 補充：

but remember, the calcium carbonate is IN EXCESS; acid is limited.

in that case, mass is not important to contribution to reaction rate; the (change of) concentration of acid is.

2012-02-22 09:42:19 補充：

rate of reaction is directly proportional to surface area; while masses of carbonate reacted in BOTH cases are the same.

• 字數太多打不下 換個帳號

R=dA/dt,Hydrochloric acid is in excess in both cases,and in the same reaction time the concentration chane of A would be eight times than B.So the time A or B comsumes more determines which reaction rate is higher.

When predicting which reaction rate is higher ,neither concentration change or reaction time interval should be set as a constant,there can be only one variable.

And the question which reaction ends first ?=Wich reaction time is shorter.

the raction time is up to experiment.you had better conduct an experiment to discover the answer.

2012-02-21 12:03:18 補充：

OK, I indeed lost the point ----spherical

I agree to 己式庚辛

You are top gun,thanks very much, .

資料來源： sky
• in this case,two factors affect which reaction fast

1.Rate is in proportional to concentration of HCl

2.Rate is in proportional to area HCl and CaCO3 contacts

Regarding the reaction as an irreversible reaction( the CO2 gas will escape the reaction beaker,leading to a closed system),we can treat this problem in Stoichiometric and kinetic terms:

1.Stoichiometric:

assuming A:CaCO3 800g B:CaCO3 100g HCl:1.0M 1Liter

CaCO3(s) + 2 HCl(aq) --> CaCl2(aq) + CO2(g) + H2O(l)

A:initial 8mol 1mol

final 7mol 0mol 1mol 1mol 1mol

B:initial 1mol 1mol

final 0mol 0mol 1mol 1mol 1mol

Hydrochloric acid is the limiting reactant,so A and B both have the same concentration change of individual chemical substances

and factor 1 are the same for A and B

(there is no relationship between The mass of CaCO3 and the chemical reation rates)

2.kinetic:

The reaction which ends first has higher reaction rate

Consider a typical chemical reaction:

aA + bB → pP + qQ , the reaction rate r for a chemical reaction

that is,reaction rate is the concentration change of a substance in a giving time

Since A and B both have the same concentration change of individual chemical substances , the rate is up to the time the reaction needs

in heterogeneous chemical reactions, reaction rates depends on collisions. The more surface area on which collisions can occur, the faster the reaction. (if they have the same amount of reactants)and the tiny pieces has more surface than the bulky ones.

So how the factor 2 determines which reaction is fast lies in how much area CaCO3 and HCl contacts,the more area they contact ,the faster the reaction,if A and B hvae the same size of spherical pieces,A ends faster.

ref:

資料來源： wiki and net paper