Custom styles help

I hope this is in the right section. If not, please accept my apologies.

I tried adding a custom style to my style.css file but found that it doesn’t span multiple paragraphs.

What I did:
I added the following custom style to my style.css file:

.tip {
    display: block;
    margin: 1em;
    padding: 4px 10px 4px 10px;
    background-color: #ebffeb;
    border: 1px solid #99cc66;
}

Then I wrote a couple of paragraphs (using the Text tab in the editor) and enclosed them in this:

<span class="tip">one paragraph here

Another paragraph here</span>

This worked fine for a single paragraph but it only works for the first paragraph when doing this with multiple paragraphs. Looking at the page source it appears that WordPress has added a “p” tag around each paragraph and that is interferring with my span.

How can I fix this to work on multiple paragraphs without the apparent break between paragraphs? I’ve likely made a noob mistake and would like to learn how to fix it.