2.1 Molecular model of an ideal gas  (Page 9/19)

Inflate a balloon at room temperature. Leave the inflated balloon in the refrigerator overnight. What happens to the balloon, and why?

In the last chapter, free convection was explained as the result of buoyant forces on hot fluids. Explain the upward motion of air in flames based on the ideal gas law.

The gauge pressure in your car tires is $2.50\times {10}^5{\text{N/m}}^2$ at a temperature of $35.0\text{°}\text{C}$ when you drive it onto a ship in Los Angeles to be sent to Alaska. What is their gauge pressure on a night in Alaska when their temperature has dropped to $-40.0\text{°}\text{C}$ ? Assume the tires have not gained or lost any air.

Suppose a gas-filled incandescent light bulb is manufactured so that the gas inside the bulb is at atmospheric pressure when the bulb has a temperature of $20.0\text{°}\text{C}$ . (a) Find the gauge pressure inside such a bulb when it is hot, assuming its average temperature is $60.0\text{°}\text{C}$ (an approximation) and neglecting any change in volume due to thermal expansion or gas leaks. (b) The actual final pressure for the light bulb will be less than calculated in part (a) because the glass bulb will expand. Is this effect significant?

People buying food in sealed bags at high elevations often notice that the bags are puffed up because the air inside has expanded. A bag of pretzels was packed at a pressure of 1.00 atm and a temperature of $22.0\text{°}\text{C}.$ When opened at a summer picnic in Santa Fe, New Mexico, at a temperature of $32.0\text{°}\text{C},$ the volume of the air in the bag is 1.38 times its original volume. What is the pressure of the air?

How many moles are there in (a) 0.0500 g of ${\text{N}}_2$ gas $(M=28.0\text{g/mol})\text{?}$ (b) 10.0 g of ${\text{CO}}_2$ gas $(M=44.0\text{g/mol})\text{?}$ (c) How many molecules are present in each case?

A cubic container of volume 2.00 L holds 0.500 mol of nitrogen gas at a temperature of $25.0\text{°}\text{C}\text{.}$ What is the net force due to the nitrogen on one wall of the container? Compare that force to the sample’s weight.

Calculate the number of moles in the 2.00-L volume of air in the lungs of the average person. Note that the air is at $37.0\text{°}\text{C}$ (body temperature) and that the total volume in the lungs is several times the amount inhaled in a typical breath as given in [link] .

An airplane passenger has $100{\text{cm}}^3$ of air in his stomach just before the plane takes off from a sea-level airport. What volume will the air have at cruising altitude if cabin pressure drops to $7.50\times {10}^4{\text{N/m}}^2$ ?

A company advertises that it delivers helium at a gauge pressure of $1.72\times {10}^7\text{Pa}$ in a cylinder of volume 43.8 L. How many balloons can be inflated to a volume of 4.00 L with that amount of helium? Assume the pressure inside the balloons is $1.01\times {10}^5\text{Pa}$ and the temperature in the cylinder and the balloons is $25.0\text{°C}$ .

According to http://hyperphysics.phy-astr.gsu.edu/hbase/solar/venusenv.html, the atmosphere of Venus is approximately $96.5\text{\%}{\text{CO}}_2$ and $3.5\text{\%}{\text{N}}_2$ by volume. On the surface, where the temperature is about 750 K and the pressure is about 90 atm, what is the density of the atmosphere?

An expensive vacuum system can achieve a pressure as low as $1.00\times {10}^{\mathrm{-7}}{\text{N/m}}^2$ at $20.0\text{°}\text{C}\text{.}$ How many molecules are there in a cubic centimeter at this pressure and temperature?

The number density N / V of gas molecules at a certain location in the space above our planet is about $1.00\times {10}^{11}{\text{m}}^{\mathrm{-3}},$ and the pressure is $2.75\times {10}^{\mathrm{-10}}{\text{N/m}}^2$ in this space. What is the temperature there?

A bicycle tire contains 2.00 L of gas at an absolute pressure of $7.00\times {10}^5{\text{N/m}}^2$ and a temperature of $18.0\text{°}\text{C}$ . What will its pressure be if you let out an amount of air that has a volume of $100{\text{cm}}^3$ at atmospheric pressure? Assume tire temperature and volume remain constant.

In a common demonstration, a bottle is heated and stoppered with a hard-boiled egg that’s a little bigger than the bottle’s neck. When the bottle is cooled, the pressure difference between inside and outside forces the egg into the bottle. Suppose the bottle has a volume of 0.500 L and the temperature inside it is raised to $80.0\text{°C}$ while the pressure remains constant at 1.00 atm because the bottle is open. (a) How many moles of air are inside? (b) Now the egg is put in place, sealing the bottle. What is the gauge pressure inside after the air cools back to the ambient temperature of $25\text{°C}$ but before the egg is forced into the bottle?

A high-pressure gas cylinder contains 50.0 L of toxic gas at a pressure of $1.40\times {10}^7{\text{N/m}}^2$ and a temperature of $25.0\text{°C}$ . The cylinder is cooled to dry ice temperature $(\mathrm{-78.5}\text{°}\text{C})$ to reduce the leak rate and pressure so that it can be safely repaired. (a) What is the final pressure in the tank, assuming a negligible amount of gas leaks while being cooled and that there is no phase change? (b) What is the final pressure if one-tenth of the gas escapes? (c) To what temperature must the tank be cooled to reduce the pressure to 1.00 atm (assuming the gas does not change phase and that there is no leakage during cooling)? (d) Does cooling the tank as in part (c) appear to be a practical solution?

Find the number of moles in 2.00 L of gas at $35.0\text{°}\text{C}$ and under $7.41\times {10}^7{\text{N/m}}^2$ of pressure.

Calculate the depth to which Avogadro’s number of table tennis balls would cover Earth. Each ball has a diameter of 3.75 cm. Assume the space between balls adds an extra $25.0\%$ to their volume and assume they are not crushed by their own weight.

(a) What is the gauge pressure in a $25.0\text{°}\text{C}$ car tire containing 3.60 mol of gas in a 30.0-L volume? (b) What will its gauge pressure be if you add 1.00 L of gas originally at atmospheric pressure and $25.0\text{°}\text{C}$ ? Assume the temperature remains at $25.0\text{°}\text{C}$ and the volume remains constant.