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估算就是不算,估算法是通过推理、猜测得出答案的一种方法。
例题:在 100 mL 0.10 mol·L-1的 AgNO3(aq) 中,加入 100 mL 溶有 2.08 g BaCl2 的溶液,
再加入 100 mL 溶有 2.50 g CuSO4·5H2O 的溶液,充分反应。下列说法中正确的是
A.最终得到白色沉淀和无色溶液
B.最终得到的白色沉淀是等物质的量的两种化合物的混合物
C.混合过程中,逸出无色气体
D.在最终得到的溶液中,c(Cu2+) = 0.01 mol·L-1
解析:本题有以下两种解法。
方法1(计算法):n(Ag+) = 0.100 L×0.10 mol·L-1 = 0.010 mol
n(Ba2+) = n (BaCl2) = = 0.0100 mol
n(Cl-) = 2n(BaCl2) = 0.0200 mol
n(SO) = n(CuSO4·5H2O) = = 0.0100 mol
首先 Cl- 与 Ag+ 发生反应生成白色 AgCl 沉淀:
Ag+ + Cl- AgCl↓
0.010 mol 0.010 mol 0.010 mol
反应后剩余 Cl-:0.0200 mol-0.010 mol = 0.010 mol。其次 Ba2+ 与 SO发生反应生
成白色 BaSO4 沉淀:
Ba2+ + SO BaSO4↓
0.010 mol 0.010 mol 0.010 mol
生成BaSO4 0.010 mol。反应后溶液中含 Cu2+,其浓度为:
c(Cu2+) == 0.033 mol·L-1
与备选项对照,可知答案。
方法2(估算法):最后 Cu2+留在溶液中,溶液浅蓝色,A 项不可选。由 CuSO4·5H2O 的质量
是3位有效数字,及溶液的体积也是3位有效数字可推知c(Cu2+)应为3位有效数字,D 项不可
选。由于溶液混合时,只发生 Ag+ 与 Cl-、Ba2+与SO的反应,所以也不会逸出气体,
C项不可选。
答案:33.4%
点评:估算法虽可大大提高解题效率,但其使用范围有一定的局限性,绝大多数计算题是不
能用估算法解决的。尝试用估算法解题是好的,但面对每一个题都想用估算法解决,有时也
会贻误时间。
练习:
1.有规律称:强酸溶液每稀释 10 倍 pH 增加 1 ,强碱溶液每稀释 10 倍 pH 减小 1,但
此规律有一定的局限性。试问将 pH = 3 的 H2SO4(aq) 稀释 105 ,其 pH 为( ).
A.8 B.7 C.2 D.3
2.将质量分数为 0.052(5.2%)的 NaOH(aq)1 L(密度为 1.06 g·cm-3)用铂电极电解,当溶
液中 NaOH 的质量分数改变了 0.010(1.0%)时停止电解,则此时溶液中应符合的关系是( ).
NaOH的质量分数
阳极析出物的质量/g
阴极析出物的质量/g
A
0.062(6.2%)
19
152
B
0.062(6.2%)
152
19
C
0.042(4.2%)
1.2
9.4
D
0.042(4.2%)
9.4
1.2
3.氢型阳离子交换树脂的主要反应可用下式表示:2R — H + M2+MR2 + 2H+,若
将 100 mL 水经过氢型阳离子交换树脂交换后,流出液用 0.10 mol·L-1的 NaOH 溶液中
和,完全反应后用去 NaOH 溶液 20 mL,若此水中存在的阳离子只有 Ca2+,则 100 mL
水中含有 Ca2+为( )
A.20.03 mg B.40 mg C.80.16 mg D.160.32 mg
4.图2—1中横坐标表示完全燃烧时耗用可燃气体 X(X = A、B、C)的物质的量 n(X),纵
坐标表示消耗 O2 的物质的量 n(O2),A、B 是两种可燃性气体 ,C 是 A、B 的混合气
体,则 C 中:n(A)∶n(B)为( )
A.2∶1 B.1∶2
C.1∶1 D.任意
2—1

参考答案:
1.提示:酸不可能稀释为碱,也不可能稀释后 pH 变小或不变。
答案:B
2.解析:电解 NaOH(aq) 的实质是电解水。随溶液中水的减少,w(NaOH)逐渐增大,因
而 C、D项不可选。电解时阳极产生 O2,阴极产生 H2,其质量前者大,后者小,故 B
项为正确答案。
答案:B
3.提示:由题意:n(Ca2+) =n(H+) =n(NaOH),根据数据可断定n(Ca2+)数值为
两位有效数字。又:m(Ca2+) = n(Ca2+)×M(Ca2+),则m(Ca2+)数值为两位有效数字。
答案: B
4.提示:首先排除任意比。由图可知: 1 mol A 耗用 0.5 mol O2,1 mol B 耗用2 mol O2;
若 A、B以1∶1混合,则 1 mol C 耗用 1.25 mol O2,而图中 1 mol C 耗用1 mol O2,可见
A、B 混合物中,n(A)∶n(B)>1∶1。观察备选项可知答案。
答案:A
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