How can I only show a widget prior to a specific date?

I assume you would like to do this through the WordPress admin and not edit your sidebar.php so here is a possible solution.

First, find out what the timestamp of August 22 was at http://www.epochconverter.com. Based on GMT time I got “1408665600”

Install the Widget Logic Plugin: https://wordpress.org/plugins/widget-logic/

Add a widget to your left sidebar. If you wanted it to be a message then a text widget might work best.

In the widget logic box of the widget, try something like the below:

get_the_date('U') <= "1408665600"

It’s saying to show the widget if the Unix timestamp of the post’s publish date is less (earlier) than or equal to the Unix timestamp of August 22, 2014.

If your widget area is shared over multiple pages and/or post types then you can also restrict it to only show when the above matches as well as the post type, something like:

get_post_type() == 'post' && get_the_date('U') <= "1408665600"

Hope that helps.