The Ministry of Education calls on students to exercise for

The Ministry of Education calls on students to exercise for an hour every day,in the hope that they will have good health to work fifty years and enjoy the whole life.为什么用in the hope that 而不用 in hope that?
这是固定短语：用定冠词的原因——后面的 of 或that 从句直接说明了hope的内容
in the hope that 怀着…的希望；希望能…
in the hope of希望；怀着……的期望；怀着希望；怀着…的期望
in the hope that希望能
in vain hope幻想地
in the hope of doing带着……的期望
in the hope of sth希望
in the hope of doing sth.怀着……的希望；怀着…的希望；怀着
in the hope of/that希望
in the hope of...怀着
而 in hope 多用作状语,相当于hopefully,修饰动词.

in the hope that: because of the wish that...
怀着。。。希望，希望能（固定用法）

特指

这个是固定的，人家的习惯是这么 说的，语言有时候没有那么多为什么，你可以查一下，没有in hope that...用的话要用in the hope that,是期望怎么怎么样的意思