Factor Label Method In a laboratory, $400 \mathrm{~L}$ of methane are stored at $600 \mathrm{~K}$ and $1.25 \mathrm{~atm}$. If the methane is forced into a 200-L tank and cooled to $300 \mathrm{~K}$, how does the pressure change?

At atmospheric pressure, a balloon contains $2.00 \mathrm{~L}$ of nitrogen gas. How would the volume change if the Kelvin temperature were only 75 percent of its original value?

Classify the following bonds as ionic, covalent, or polar covalent using electronegativity values. (Chapter 9 ) a) $\mathrm{NH}$ c) $\mathrm{BH}$ b) $\mathrm{BaCl}$ d) $\mathrm{NaI}$

Find the particular antiderivative of the following derivative that satisfies the given condition:

$$a)\;\frac{dy}{dx}=5x^{-4}+4x^{-1}-1,\;y(1)=0,\;\;b)\;\frac{dx}{dt}=7e^t-5,\;x(0)=1.$$

Can an atom of an element have six electrons in the $2 p$ sublevel?

Overloaded Why do tire manufacturers recommend that tire pressure be increased if the recommended number of car passengers or load size is exceeded?

A vessel of volume 22.4 dm$^3$ contains 2.0 mol $\ce{H2}$ and 1.0 mol $\ce{N2}$ at 273.15 K. Calculate:

(a) The mole fractions of each component.

(b) The total pressure in a vessel.

(c) The partial pressures of $\ce{H2}$ and $\ce{N2}$.

Commercially, compressed oxygen is sold in metal cylinders. If a 120-L cylinder is filled with oxygen to a pressure of 134 bar at $22^{\circ} \mathrm{C}$, what is the mass of $\mathrm{O}_2$ present? How many liters of $\mathrm{O}_2$ gas at $1.00$ bar and $22^{\circ} \mathrm{C}$ could the cylinder produce? (Assume ideal behavior.)

(b) A certain gas obeys the van der Waals equation with a=0.76 m$^6$ Pa mol$^{-2}$. Its volume is found to be $4.00 \times 10^{-4} \mathrm{~m}^3 \mathrm{~mol}^{-1}$ at $288 \mathrm{~K}$ and $4.0 \mathrm{MPa}$. From this information calculate the van der Waals constant $b$. What is the compression factor for this gas at the prevailing temperature and pressure?

(a) A certain gas obeys the van der Waals equation with $a = 0.50 m^6$ Pa $mol^{−2}.$ Its volume is found to be $5.00 \times 10 ^ { - 4 } \mathrm { m } ^ { 3 } \mathrm { mol } ^ { - 1 }$ at 273 K and 3.0 MPa. From this information calculate the van der Waals constant b. What is the compression factor for this gas at the prevailing temperature and pressure? (b) A certain gas obeys the van der Waals equation with a = 0.76 $m^6$ Pa $mol^{−2}.$ Its volume is found to be $4.00 \times 10 ^ { - 4 } \mathrm { m } ^ { 3 } \mathrm { mol } ^ { - 1 }$ at 288 K and 4.0 MPa. From this information calculate the van der Waals constant b. What is the compression factor for this gas at the prevailing temperature and pressure?

The atmosphere on Mars is composed mainly of carbon dioxide. The surface temperature is 220 K and the atmospheric pressure is about 6.0 mmHg. Taking these values as Martian “STP,” calculate the molar volume in liters of an ideal gas on Mars.

A cylinder containing $32 \mathrm{~g}$ of oxygen gas is placed on a balance. The valve is opened and $16 \mathrm{~g}$ of gas are allowed to escape. How will the pressure change?

Explain why balloons filled with helium rise in air but balloons filled with carbon dioxide sink.

What are allotropes? Name three elements that occur as allotropes.