Coil balances for bathroom window

A home owner from Colorado says:
My Sister has a double hung window in her bathroom. The top portion is fixed. The coil balances have broken see third photo. The dimensions of the bottom half are shown in the first photo with the barcode. The movable window weighs 8.8 pounds. The distance from the screw hole to fix the coil balance to the bottom of the sash is 2'-5 3/4". What size, load capacity coil do I need. Also the screw hole is flush with the inside of the window frame. How do I prevent putting the coil balance in a bind when attaching it to the bracket.
Thanks, Al
User submitted photos of window hardware.
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Paul from SWISCO responded:
Thanks for posting. Start by looking at our 15-087 shoe, 16-024 bracket, and Series 180 coil spring. Also be sure to see our 33-072 screw if you can't re-use yours. I believe this hardware should match what you have. As for what strength spring you need, it could be our S180-5. Each of these springs, individually, can carry 5 pounds. So two working together can carry 10 pounds. I believe your sash is around 9 pounds, so this should be perfect. Let me know what you think.
A quick learner from Colorado says:

Just a couple of questions from your post. The mounting bracket P/N 16-024 will mount flush on the inside of the window jamb. will that be a problem for attaching the coil balance and keeping it aligned?
Second, is the 180-5 coil balance long enough to accommodate the distance from the bottom of the window to the mounting bracket screw hole of roughly 30 inches?
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Tom from SWISCO responded:
See our diagram below to get an idea of how the 16-024 is meant to be installed. As for the travel, the length of the Series 180 is actually around 35" so it should be more than enough.
Diagram of 15-087
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