An appeal to ethos is an appeal to convince the audience of the credibility and character of the author. In this case, in order to convince your mother, you would need to make a statement that makes you look credible and moral. For example, you could refer to your sense of responsibility, which will lend credibility to your position. A potential sentence could be:
"I cannot go grocery shopping because it is my duty to study for school, and nothing is more important than my education."