让公众头疼的“浓度问题”巧解办法来了
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;">在义务教育<span style="color: black;">周期</span>，数学学科中有<span style="color: black;">这般</span>一类问题。它是让每一届的<span style="color: black;">非常多</span>学生头疼的问题，<span style="color: black;">亦</span>是考试常考的题型，它<span style="color: black;">便是</span>——<strong style="color: blue;">浓度问题</strong>。</p>
<div style="color: black; text-align: left; margin-bottom: 10px;"><img src="https://p3-sign.toutiaoimg.com/dfic-imagehandler/85a6948f-3261-4676-8542-8df6fdb95aa3~noop.image?_iz=58558&from=article.pc_detail&lk3s=953192f4&x-expires=1724049420&x-signature=fRGYq%2Bil3LmjfF69MuyTfHaYBEU%3D" style="width: 50%; margin-bottom: 20px;"></div>
<h1 style="color: black; text-align: left; margin-bottom: 10px;">什么是浓度问题呢？</h1>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><span style="color: black;">咱们</span>以盐水为例，像盐<span style="color: black;">这般</span>能溶解在水<span style="color: black;">或</span>其它液体中的纯净物质叫做<strong style="color: blue;"><span style="color: black;">溶质</span></strong>；像水<span style="color: black;">这般</span>能用来溶解物质的纯净液体叫做<strong style="color: blue;"><span style="color: black;">溶剂</span></strong>；溶质与溶液的混合物叫做<strong style="color: blue;"><span style="color: black;">溶液</span></strong>，溶质在溶液中所占的百分比叫做<strong style="color: blue;"><span style="color: black;">浓度</span></strong>，<span style="color: black;">亦</span>叫做<strong style="color: blue;"><span style="color: black;">百分比浓度</span></strong>。</p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;">关于浓度问题<span style="color: black;">平常</span>的数量关系有：</p>溶液质量 ＝ 溶质质量 + 溶剂质量浓度 ＝ 溶质质量 ÷ 溶液质量 × 100%溶液质量 ＝ 溶质质量 ÷ 浓度溶质质量 ＝ 溶液质量 × 浓度<div style="color: black; text-align: left; margin-bottom: 10px;"><img src="https://p3-sign.toutiaoimg.com/pgc-image/ca694207a5b14404a016acdf9454958e~noop.image?_iz=58558&from=article.pc_detail&lk3s=953192f4&x-expires=1724049420&x-signature=Ju%2BBDx%2BVIF6d5tIjEBXGcXrbSD0%3D" style="width: 50%; margin-bottom: 20px;"></div>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;">简单来理解<span style="color: black;">便是</span>，20克盐（溶质）溶解在80克水（溶剂）<span style="color: black;">其中</span>，这杯盐水的浓度<span style="color: black;">便是</span> 20 ÷ （20 + 80）× 100%＝20%</p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><strong style="color: blue;">介绍完浓度的问题后，让<span style="color: black;">咱们</span>看一道例题。</strong></p>
<h1 style="color: black; text-align: left; margin-bottom: 10px;">1号杯盐水溶液有80克，它的浓度为40%，2号杯盐水溶液有120克，它的浓度为15%，两个杯子的溶液混合在<span style="color: black;">一块</span>后形成的新溶液浓度为多少？</h1>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><strong style="color: blue;">解法1（传统解法）</strong></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><span style="color: black;">首要</span>找到题目中<span style="color: black;">必须</span>的所有溶质</p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;">1号杯溶质质量 ＝ 80 × 40% ＝32（克）</p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;">2号杯溶质质量 ＝ 120 × 15% ＝18（克）</p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;">新溶液的浓度 ＝ （32 + 18）÷ （80 + 120）× 100% ＝25%</p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><strong style="color: blue;">解法2（十字相乘法）</strong></p>
<div style="color: black; text-align: left; margin-bottom: 10px;"><img src="https://p3-sign.toutiaoimg.com/pgc-image/4c22c07080584f9195361805188ac170~noop.image?_iz=58558&from=article.pc_detail&lk3s=953192f4&x-expires=1724049420&x-signature=wVOPhJ7AEkEjF%2F52nNKT0pKF7Gw%3D" style="width: 50%; margin-bottom: 20px;"></div>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;">按上图的形式先写出对应的数据，<span style="color: black;">咱们</span>设新溶液的浓度为x。</p>
<div style="color: black; text-align: left; margin-bottom: 10px;"><img src="https://p3-sign.toutiaoimg.com/pgc-image/4f340da01e08421aa8aa1084eb5ce6ca~noop.image?_iz=58558&from=article.pc_detail&lk3s=953192f4&x-expires=1724049420&x-signature=1HQtuSYkEDwHixrQa%2BaNbnI7sJ8%3D" style="width: 50%; margin-bottom: 20px;">
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;">写出的上面数据要满足以上公式</p>
</div>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;">把数据按上图的形式填写如下：</p>
<div style="color: black; text-align: left; margin-bottom: 10px;"><img src="https://p3-sign.toutiaoimg.com/pgc-image/6135cdee3ff24265a24fa622be8bab8d~noop.image?_iz=58558&from=article.pc_detail&lk3s=953192f4&x-expires=1724049420&x-signature=18aXQOrsRbCq9pjfPBh2WmSr1xw%3D" style="width: 50%; margin-bottom: 20px;"></div>
<div style="color: black; text-align: left; margin-bottom: 10px;"><img src="https://p3-sign.toutiaoimg.com/pgc-image/4ed9db05ba7f4fe6a3627929ec887816~noop.image?_iz=58558&from=article.pc_detail&lk3s=953192f4&x-expires=1724049420&x-signature=hD8%2Bg7y9%2FoF06YMGjJOmkKnDx0M%3D" style="width: 50%; margin-bottom: 20px;"></div>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;">解上图中的方程求得：x ＝ 25% </p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><strong style="color: blue;">总结：本文介绍了两种求解混合浓度的<span style="color: black;">办法</span>，<span style="color: black;">大众</span><span style="color: black;">能够</span>针对自己的<span style="color: black;">爱好</span><span style="color: black;">选取</span>自己<span style="color: black;">爱好</span>的<span style="color: black;">办法</span>求解此类题目。<span style="color: black;">倘若</span>是<span style="color: black;">选取</span>题的话，其实还<span style="color: black;">能够</span><span style="color: black;">按照</span><span style="color: black;">混合溶液的浓度介于混合前两种溶液的浓度之间，且偏向于量大的一方</span>（<span style="color: black;">由于</span>一杯开水和一杯凉水混合，水温<span style="color: black;">必定</span>比开水低，比凉水高）来排除部分答案。</strong></p>
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