Molecules of a gas in a container are moving around at different speeds. Maxwell's speed distribution law gives the probability distribution P(v) as a function of temperature and speed:

$$P ( v ) = 4 \pi \left( \frac { M } { 2 \pi R T } \right) ^ { 3 / 2 } v ^ { 2 } e ^ { \left( - M v ^ { 2 } \right) / ( 2 R 7 ) }$$

where M is the molar mass of the gas in kg/mol, R = 8.31 J/(mol K), is the gas constant, Tis the temperature in kelvins, and vis the molecule's speed in m/s. Make a $3 - \mathrm { D }$ plot of $P ( v )$ as a function of $v$ and $T$ for $0 \leq v \leq 1000 \mathrm { m } / \mathrm { s }$ and $70 \leq T \leq 320 \mathrm { K }$ for oxygen (molar mass 0.032$\mathrm { kg } / \mathrm { mol } )$ .

The pressure of a quantity of ideal gas was held constant at 764 newtons per square meter. The original temperature was $200^{\circ} \mathrm{C}$, and the original volume was $400 \mathrm{ml}$. If the temperature was increased to $600^{\circ} \mathrm{C}$, what was the final volume? Begin by solving for $V_2$. Then add 273 to convert degrees Celsius to kelvins.

Research the significance of the following number.

  5 millions

The ideal gas equation states that

$$P = \frac { n R T } { V }$$

where P is the pressure, V is the volume, T is the temperature, R = 0.08206 (L atm)/(mol K) is the gas constant, and n is the number of moles. Real gases, especially at high pressure, deviate from this behavior. Their response can be modeled with the van der Waals equation

$$P = \frac { n R T } { V - n b } - \frac { n ^ { 2 } a } { V ^ { 2 } }$$

where a and b are material constants. Consider 1 mole ( n = 1 ) of nitrogen gas at T = 300K. (For nitrogen gas a = 1.39 ($L^2$ atm)/mol$^2$, and b = 0.0391 L/mol.) Create a vector with values of Vs for $0.1\leq V\leq 1$ L, using increments of 0.02 L. Using this vector calculate P twice for each value of V, once using the ideal gas equation and once with the van der Waals equation. Using the two sets of values for P, calculate the percent of error $\left( \frac { P _ { \text { waal } } - P _ { \text {waals} } } { P _ { \text {waals} } } 100 \right)$ for each value of V. Finally, by using MATLAB's built-in function max, determine the maximum error and the corresponding volume.

An ideal gas has a density of $0.0899 \mathrm{~g} / \mathrm{L}$ at $20.00^{\circ} \mathrm{C}$ and $101.325 \mathrm{kPa}$. Identify the gas.

The accompanying figure shows the graph of the pressure p in atmospheres (atm) versus the volume $V$ in liters (L) of 1 mole of an ideal gas at a constant temperature of $300 \mathrm{~K}$ (kelvins). Use the line segments shown in the figure to estimate the rate of change of pressure with respect to volume at the points where $V=10 \mathrm{~L}$ and $V=25 \mathrm{~L}$.

If 45.98 g of sodium combines with an excess of chlorine gas to form 116.89 g of sodium chloride, what mass of chlorine gas is used in the reaction?

Research one medical or industrial use of liquefied gases.

(a) Briefly explain how the gas is liquefied.

(b) Explain how the gas is used in this application.

One mole of nitrogen gas and one mole of oxygen gas contain the same number of entities under the same conditions of temperature and pressure.

What is the normative strategy to selecting treatment targets?

An aqueous solution of ammonia, $\mathrm{NH}_3(\mathrm{aq})$, can be broken down by electrolysis into pure nitrogen gas, $\mathrm{N}_2(\mathrm{~g})$, and pure hydrogen gas, $\mathrm{H}_2(\mathrm{~g})$.

(a) Write the balanced chemical equation for the decomposition of ammonia.

(b) Predict the ratio of the volumes of nitrogen gas to hydrogen gas produced, assuming the same temperature and pressure for each gas. Explain your prediction.

Why is informed consent necessary for ethical research?

Suppose we wish to inflate a weather balloon with helium. The balloon should have a volume of $100 \mathrm{m}^{3}$ when inflated to a pressure of 0.10 bar. If we use 50.0-liter cylinders of compressed helium gas at a pressure of 100 bar, how many cylinders do we need? Assume that the temperature remains constant.

The bulk modulus $B$ of a material can be defined by $B=-V \partial P / \partial V \quad.Use the monatomic ideal-gas relation$P V=$\frac{2}{3}$ N E_{a v}$, where$E_{a x}$is the average kinetic energy, Equation 38 22 and Equation$38-23$to show that$P=$\frac{2}{5}$ N E_${\mathrm{F}}$ / V=C V=5 / 3$, where$C$is a constant independent of$V$.