A gas made up of atoms escapes through a pinhole 2.04 times as fast as kr gas. write the chemical formula of the gas.

The chemical formula for the unknown gas is Ne. Since we're looking for the rate at which a gas escapes through a small hole, we're dealing with effusion. For effusion, the rate is proportional to the velocity of the gas particles. Kinetic energy E = 0.5 mv^2 Since the kinetic energy of individual gas particles is the same if their temperatures are the same, we can create the following equality: 0.5 m1 (v1) ^2 = 0.5 m2 (v2) ^2 Double each side to make it simplier. m1 (v1) ^2 = m2 (v2) ^2 Divide both sides by m1 and by (v2) ^2, giving (v1) ^2 / (v2^2) = m2/m1 And take the square root, giving (v1) / (v2) = sqrt (m2/m1) Now let's use the value 1 and the atomic weight of Kr for v1 and m1 1 / (v2) = sqrt (m2/83.798) And for v2, we'll use the value 2.04 1/2.04 = sqrt (m2/83.798) Now solve for m2. 1/2.04 = sqrt (m2/83.798) 1/4.1616 = m2/83.798 83.798/4.1616 = m2 20.13600538 = m2 So the atomic weight of the unknown gas should be close to 20.136. Looking at a periodic table, I find that neon has an atomic weight of 20.18 which is quite close. Additionally, since neon is a noble gas, its gas particles consist of individual atoms. So the unknown gas is neon.