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(e.g., water) based on pressure and temperature. The critical point represents the maximum temperature and pressure where the substance can be a liquid. Below the critical temperature, a gas can become a liquid.

The critical temperature for a substance is the temperature at which it cannot condense into a liquid, regardless of the pressure. There is also a critical pressure, which is the pressure at which the substance cannot boil, regardless of the temperature. The intersection of the two lines on the diagram represents the triple point, which is the temperature and pressure at which a substance coexists as a solid, liquid, and gas. This is used to define the Kelvin temperature scale. The triple point of water is at a pressure of 6.105 millibars and a temperature of 273.16 Kelvin. Below the triple point, a substance can exist only as a gas or a solid, and it transitions directly from one to the other, a process known as sublimation or deposition. The triple point of water is used as a reference point for maps of Mars because liquid water cannot exist at altitudes above the triple point pressure. This is important for searching for evidence of life on Mars.

The kinetic theory of gases explains the behavior of gases based on the motion of their particles. The root mean square speed is a measure of the average speed of the gas particles. Phase changes, such as the critical point and the triple point, have significant implications for understanding the behavior of substances.

Crash Course Physics is a series produced in association with PBS Digital Studios. You can find more episodes on their channel, including shows like PBS Idea Channel, Brain Craft, and Shank's FX. This episode was filmed in the Crash Course Studio with the help of an amazing team.

A 27.67 gram sample of iron is heated in the presence of excess chlorine. A metal chloride is formed with a mass of 62.79 g. Determine the empirical formula of the metal chloride.

Pure cyclohexane, C6H12, has a molar mass of 84.161 g mol-1 and a density of 0.7785 g mL-1, a freezing point of 6.53°C, and a boiling point of 80.72°C. Its freezing point depression and boiling point elevation constants are: Kf = 20.0 °C m -1; Kb = 2.69°C m -1. A solution was made by taking 15.46 g of an unknown nonelectrolyte and dissolving it in 125.0 g of cyclohexane. The measured freezing point of the solution was 4.28°C. Calculate the molar mass of the unknown substance.

A solution is made by dissolving 0.532 mol of nonelectrolyte solute in 775 g of benzene. Calculate the freezing point and boiling point of the solution.

Constants for freezing-point depression and boiling-point elevation calculations at 1 atm:

Pure benzene, C₆H₆, has a molar mass of 78.114 g mol^-1, a density of 0.8765 g mL^-1, a freezing point of 5.45^°C, and a boiling point of 80.2^°C. Its freezing point depression and boiling point elevation constants are: K_f = 5.07^°C m^-1; K_b = 2.53^oC m^-1. A solution was made by taking 33.88 g of an unknown nonelectrolyte and dissolving it in 175.0 g of benzene. The measured freezing point of the solution was 1.65^oC. Calculate the molar mass of the unknown substance.

A mixture is prepared that is 5.0% (w/w) of an unknown substance mixed with naphthalene (molar mass = 128.2 g mol^-1). The freezing
point of this mixture is found to be 77.3 °C. What is the molar mass of the unknown substance? (The melting point of naphthalene is 80.2 °C and Kf = 6.9 °C m^-1.)
The molar mass of the unknown substance =

A compound with a cubic structure, BaxTiyOz, is projected. below:

   (i) Find out the compound's stoichiometry. (ii) What are the Ti, O, and Ba ions' coordination numbers and geometries? (iii) Determine the kind of structure that this compound has chosen. (iv) Draw a projection using linked polyhedra to depict the "TiyOz" portion of the structure (i.e., identify the Ti-based polyhedra and demonstrate how these are linked together in the structure). (v) Make a suggestion for a preparation technique for this compound. One point (vi) What color does the compound have? 

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