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Chapter 10: Problem 37

Calculate the number of molecules in a deep breath of air whose volume is \(2.25 \mathrm{~L}\) at body temperature, \(37^{\circ} \mathrm{C}\), and a pressure of 735 torr.

Short Answer

Expert verified
There are approximately \(4.93 脳 10^{22}\) molecules in a deep breath of air whose volume is 2.25 L at body temperature and pressure of 735 torr.

Step by step solution

01

Convert pressure unit from torr to atm and volume unit to dm鲁.

To use the ideal gas law equation, we should convert the pressure in torr into atm and the volume in liters to dm鲁. 1 atm = 760 torr 1 L = 1 dm鲁 So, Pressure (P) = 735 torr 脳 (1 atm / 760 torr) = 0.9671 atm Volume (V) = 2.25 L = 2.25 dm鲁
02

Convert temperature to Kelvin.

In order to use the ideal gas law equation, we need to convert the temperature from Celsius to Kelvin. Temperature (T) = 37掳C + 273.15 = 310.15 K
03

Use the ideal gas equation to find the number of moles.

Now we can use the ideal gas law equation to find the number of moles (n). The ideal gas constant (R) is given in the units of L路atm/mol路K or dm鲁路atm/mol路K, which is 0.0821 dm鲁路atm/mol路K. \(PV = nRT\) n = PV / RT n = (0.9671 atm) 脳 (2.25 dm鲁) / [(0.0821 dm鲁路atm/mol路K) 脳 (310.15 K)] n = 0.0819 moles
04

Calculate the number of molecules using Avogadro's number.

Now that we have the number of moles, we can convert it into the number of molecules using Avogadro's number, which is approximately 6.022 脳 10虏鲁 molecules/mol. Number of molecules = n 脳 Avogadro's number Number of molecules = 0.0819 moles 脳 (6.022 脳 10虏鲁 molecules/mol) Number of molecules = 4.93 脳 10虏虏 molecules There are approximately \(4.93 脳 10^{22}\) molecules in a deep breath of air whose volume is 2.25 L at body temperature and pressure of 735 torr.

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Most popular questions from this chapter

Many gases are shipped in high-pressure containers. Consider a steel tank whose volume is \(65.0 \mathrm{~L}\) and which contains \(\mathrm{O}_{2}\) gas at a pressure of \(16,500 \mathrm{kPa}\) at \(23^{\circ} \mathrm{C}\). (a) What mass of \(\mathrm{O}_{2}\) does the tank contain? (b) What volume would the gas occupy at STP? (c) At what temperature would the pressure in the tank equal \(150.0 \mathrm{~atm} ?\) (d) What would be the pressure of the gas, in \(\mathrm{kPa}\), if it were transferred to a container at \(24^{\circ} \mathrm{C}\) whose volume is \(55.0 \mathrm{~L} ?\)

(a) Calculate the density of sulfur hexafluoride gas at 707 torr and \(21^{\circ} \mathrm{C}\). (b) Calculate the molar mass of a vapor that has a density of \(7.135 \mathrm{~g} / \mathrm{L}\) at \(12{ }^{\circ} \mathrm{C}\) and 743 torr.

Complete the following table for an ideal gas: $$ \begin{array}{llll} \hline \boldsymbol{P} & \boldsymbol{V} & \boldsymbol{n} & \boldsymbol{T} \\ \hline 2.00 \mathrm{~atm} & 1.00 \mathrm{~L} & 0.500 \mathrm{~mol} & ? \mathrm{~K} \\ 0.300 \mathrm{~atm} & 0.250 \mathrm{~L} & ? \mathrm{~mol} & 27^{\circ} \mathrm{C} \\ 650 \text { torr } & ? \mathrm{~L} & 0.333 \mathrm{~mol} & 350 \mathrm{~K} \\ ? \mathrm{~atm} & 585 \mathrm{~mL} & 0.250 \mathrm{~mol} & 295 \mathrm{~K} \\ \hline \end{array} $$

For nearly all real gases, the quantity \(P V / R T\) decreases below the value of 1, which characterizes an ideal gas, as pressure on the gas increases. At much higher pressures, however, \(P V / R T\) increases and rises above the value of 1 . (a) Explain the initial drop in value of \(P V / R T\) below 1 and the fact that it rises above 1 for still higher pressures. (b) The effects we have just noted are smaller for gases at higher temperature. Why is this so?

A fixed quantity of gas at \(21{ }^{\circ} \mathrm{C}\) exhibits a pressure of 752 torr and occupies a volume of \(4.38 \mathrm{~L}\). (a) Use Boyle's law to calculate the volume the gas will occupy if the pressure is increased to \(1.88 \mathrm{~atm}\) while the temperature is held constant. (b) Use Charles's law to calculate the volume the gas will occupy if the temperature is increased to \(175^{\circ} \mathrm{C}\) while the pressure is held constant.
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