Two vessels are labeled a and b. vessel a contains nh3 gas at 70°c, and vessel b contains he gas at the same temperature. if the average kinetic energy of nh3 is 7.1x10^(-21) j/molecule, calculate the mean-square speed of he atoms in m^2/s^2.

v² = 2.14 × 10⁶ m²/s²

Explanation:

1) Since the average kinetic energy of a gas is only dependent on its temperature, you conclude that, at the same temperature of 70°C, the average kinetic energy of He atoms is the same that the average kinetic energy of NH₃ molecules: 7.1 × 10⁻²¹ J / molecule.

2) Now, you can use the equation that relates the average kinetic energy with the mean-square speed:

KE avg = (1/2)mv²

Where:

Ke avg is the average kinetic energy,m is the mass, andv² is the mean-square speed.

You need to use the atomic mass of helium to find the mass (average) of one atom of helum:

Atomic mass of helium: 4.003 g / molaverage mass of 1 atom:

        m = 4.003 g/ mol / (6.022 × 10²³ atoms/mol)

        m = 6.647 × 10⁻²⁴ g = 6.647 10 ⁻²⁷ kg / atom

3) Solve for v², substitute, and compute:

Note: since He is a monoatomic molecule, kg/atom = kg/molecule.

KE avg = (1/2)mv² ⇒ v² = 2KE avg / mv² = 2 × 7.1 × 10⁻²¹ J/ molecule /  (6.647 × 10 ⁻²⁷ kg / molecule)

            = 2.14 × 10⁶ m²/s² ← answer

The answer to your question really depends on three things: how much water you have, how cold it is to start out, and how cold the things around it are. water actually freezes when it gets to 32 degrees fahrenheit (0 degrees celsius), but the time it takes to get there may be different.  let's start with the first. if you take two glasses, and fill one with a tiny bit of water, and the other about halfway, then put them both in the freezer, the one with less water will freeze first (you can try this at home, but i recommend using plastic cups and not glass ones).  now let's move on to the second part. let's say you have two glasses, and you fill one with really cold water that has been in the refrigerator, and the other with really hot water from the sink. if you put both of them in the freezer, the one that started out colder will freeze first.  for the third part, let's imagine that you have two glasses with the same amount of water in them, and the water is at the same temperature. imagine putting one outside on a really really cold day in georgia, and having a friend in alaska put one outside on the same day. since it would be so much colder in alaska, the glass of water there would freeze before yours.  so, if you took a tiny bit of really cold water in a glass, and put it outside on a cold day in alaska, it would freeze a lot faster than a big glass of hot water outside on a cold day in georgia.