Question

A hot air balloon is filled with 1.13 × 106 L of an ideal gas on a cool morning (11 °C). The air is heated to 111 °C. What is the volume of the air in the balloon after it is heated? Assume that none of the gas escapes from the balloon.

At a certain temperature and pressure, one liter of CO2 gas weighs 1.15 g. What is the mass of one liter of CH4 gas at the same temperature and pressure?

A flexible container at an initial volume of 3.10 L contains 2.51 mol of gas. More gas is then added to the container until it reaches a final volume of 14.1 L. Assuming the pressure and temperature of the gas remain constant, calculate the number of moles of gas added to the container.

How many moles are present in 0.529 L of hydrogen gas at 51.8 °C and 729 Torr? Assume ideal behavior

If an ideal gas has a pressure of 4.73 atm, a temperature of 24.91 °C, and has a volume of 39.93 L, how many moles of gas are in the sample?

A sample of an ideal gas has a volume of 2.32 L at 278 K and 1.08 atm. Calculate the pressure when the volume is 1.94 L and the temperature is 308 K.

1.15 g of an unknown gas at 21 °C and 1.00 atm is stored in a 1.95-L flask

A mixture of He, Ne, and Ar has a pressure of 21.7 atm at 28.0 °C. If the partial pressure of He is 2.24 atm and that of Ar is 4.28 atm, what is the partial pressure of Ne?

A gas cylinder contains 1.20 mol He, 1.70 mol Ne, and 1.40 mol Ar. If the total pressure in the cylinder is 2350 mmHg, what is the partial pressure of each of the components? Assume constant temperature.

A 7.55-L container holds a mixture of two gases at 15 °C. The partial pressures of gas A and gas B, respectively, are 0.250 atm and 0.505 atm. If 0.140 mol of a third gas is added with no change in volume or temperature, what will the total pressure become?

A sample of oxygen gas was collected via water displacement. Since the oxygen was collected via water displacement, the sample is saturated with water vapor. If the total pressure of the mixture at 26.4 °C is 749 torr, what is the partial pressure of oxygen? The vapor pressure of water at 26.4 °C is 25.81 mm Hg.

The combustion of octane, C8H18, proceeds according to the reaction

2 C8H18(l) + 25 O2(g) --> 16 CO2(g) + 18 H2O(l)

If 538 mol of octane combusts, what volume of carbon dioxide is produced at 14.0 �C and 0.995 atm?

chlorine gas can be prepared in the laboratory by the reaction of manganese dioxide with hydrochloric acid, HCl (aq), as described by the chemical equation... MnO2(s) + 4HCl(aq) -----> MnCl2(aq) + 2H2O(l) + Cl2(g) How much MnO2(s) grams, should be added to the excess HCl(aq) to obtain 145 mL of Cl2(g) at 25 Celsius and 765 Torr? (g MnO2) Please give all of the formulas with conversions and explanations.

A ballon is filled with 69.8 g of Ar. The gas is at STP. Calculate the volume of the Ar gas in liters. Refer to the periodic table.

Answer 1

A hot air balloon is filled with 1.13 × 106 L of an ideal gas on a cool morning (11 °C). The air is heated to 111 °C. What is the volume of the air in the balloon after it is heated? Assume that none of the gas escapes from the balloon.

Ans1: Using ideal gas equation,

        

                     PV=nRT

We assume that the same number of moles of a gas create same pressure on the wall of the balloon. Hence,          

         At constant P and n

                 V₂/V₁ = T₂/T₁ ……………..(1)

Given, V₁ = 1.13x10⁶ L

            T₁ = 11^o C = (273+11) K = 284 K

            T₂ = 111 ^o C = (273+111) K = 384 K

Using (1), we get

            V₂ = 384 Kx1.13x10⁶ L/284 K = 1.53 x10⁶ L

Hence, the volume of the air in the balloon is 1.53 x10⁶ L after it is heated.

At a certain temperature and pressure, one liter of CO2 gas weighs 1.15 g. What is the mass of one liter of CH₄ gas at the same temperature and pressure?

Ans2: At constant temperature and pressure, same volume of the gases has same number of moles. Here volume of both CO₂ and CH₄ is one liter. So, Number of moles of CO₂ is equal to number of moles of CH₄.

              Number of moles = Mass/Molar mass

              Number of moles of CO₂ = (1.15 g)/(44 g/mol) = 2.614x10^-2 mol

              Number of moles of CH₄ = 2.614x10^-2 mol

               Mass of CH₄ = 2.614x10^-2 mol x 16 g/mol = 0.418 g

Hence, the mass of one liter of CH₄ gas is 0.418 g at the same temperature and pressure.

              

A flexible container at an initial volume of 3.10 L contains 2.51 mol of gas. More gas is then added to the container until it reaches a final volume of 14.1 L. Assuming the pressure and temperature of the gas remain constant, calculate the number of moles of gas added to the container.

Ans3: We know that at constant pressure and temperature, volume is directly proportional to the number of mole of the gas.

                         V₂/V₁ = n₂/n₁

Given,   V₁ = 3.10 L, n₁ = 2.51 mol, V₂ = 14.1 L

ð             n₂ = (14.1 L)x(2.51 mol)/(3.10 L) = 11.42 mol

Number of moles added to the system is final number of moles minus initial number of moles.

Number of moles added = n₂-n₁ = 11.42 mol - 2.51 mol = 8.91 mol

Hence, the number of moles of gas added to the container is 8.91 mol.    

How many moles are present in 0.529 L of hydrogen gas at 51.8 °C and 729 Torr? Assume ideal behaviour

Ans4: Use the ideal gas equation,

                       PV = nRT    ……….(1)

           Given, P = 729 Torr = 729/760 atm = 0.959 atm [1 atm = 760 Torr]

                       V = 0.529 L

                       T = 51.8 °C = (51.8+273) = 324.8 K

                       R = 0.0821 L-atm/mol-K

Putting this in equation (1)

                       

                       n = (0.959 atm x 0.529 L)/( 0.0821 L-atm/mol-Kx324.8 K)

                          = 1.9x10^-2 mol

Hence, number of moles of hydrogen gas present in the system is 1.9x10^-2 mol.

                          

If an ideal gas has a pressure of 4.73 atm, a temperature of 24.91 °C, and has a volume of 39.93 L, how many moles of gas are in the sample?

Ans5: Use the ideal gas equation,

                       PV = nRT    ……….(1)

           Given, P = 4.73 atm

                       V = 39.93 L

                       T = 24.91°C = (24.91+273) = 297.91K

                       R = 0.0821 L-atm/mol-K

Putting this in equation (1)

                       

                       n = (4.73 atm x 39.93 L)/( 0.0821 L-atm/mol-Kx297.91K)

                          = 7.72 mol

Hence, number of moles of hydrogen gas present in the sample is 7.72 mol.

A sample of an ideal gas has a volume of 2.32 L at 278 K and 1.08 atm. Calculate the pressure when the volume is 1.94 L and the temperature is 308 K.

Ans6: We know from the ideal gas equation that the relation between the two different temperature, pressure and volume at constant number of mole or for same gas.

                     P₁V₁/T₁ = P₂V₂/T₂ ……………..(1)

Given,            P₁ = 1.08 atm    P₂ = ?   

                       V₁ = 2.32 L       V₂ = 1.94 L

                       T₁ = 278 K         T₂ = 308 K

Putting in (1), we get

                      

                    (1.08 atm)(2.32 L)/(278K) = P₂ (1.94 L)/(308K)

                       

                     P₂ = (1.08 atmx2.32 Lx308K)/ (278Kx1.94 L)

                     P₂ = 1.43 atm

Hence, the pressure is 1.43 atm when the volume is 1.94 L and the temperature is 308 K.