I am planning on flying from DC , USA to Nur-Sultan, KZ With Air China. I will have layover of 22 h

If you are flying a combination of CA818 and CA791, you are definitely eligible for 24 hour visa free transit in Beijing and you don't need any kind of visa. You will just print out your flight tickets and have those printouts with you. Also, you will declare at check-in in Washington that you will travel to Nur-Sultan, Kazakhstan via Beijing using 24 hour visa free transit. After a short inspection of your flight tickets, you will be allowed to board the plane. You will also ask whether your luggage will be tagged all the way to your final destination.

Upon arrival in Beijing, you will approach 24 hour visa free transit where you will apply (for free) for a temporary entry permit to be allowed to exit the airport. You are advised to book your accommodation in Beijing in advance and to bring with you a confirmation printout about this accommodation booking. This will significantly increase your chances to be granted a permit. Anyway, you should be aware that the issuing of a temporary entry permit always depends on immigration discretion on a day of arrival.