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4. Calculate the number of gas molecules in a container of volume 0.30 m filled with gas under a partial vacuum of pressure 15 Pa at 17 .C. 5. What is the volume occupied by 4.40 g of hydrogen gas under a pressure of 2.80 atm and a temperature of 20 .C? m3 6. A steel-belted radial automobile tire is inflated to a gauge pressure of 2.15 x 10 Pa when the temperature is 63 F. Later in the day, the temperature rises to 97 OF. Assuming the volume of the tire remains constant, what is the gauge pressure at the elevated temperature? [Hint: Remember that the ideal gas law uses absolute pressure.] Pa 7. Two ideal gases have the same mass density and the same absolute pressure. One of the gases is helium (He), and its temperature is 178 K. The other gas is neon (Ne). What is the temperature of the neon?(The molar mass of Helium is 4.0026 g and that one of Neon is 20.1797 9) K 8. A rigid tank contains 71.5 g of chlorine gas (Cl2) at a temperature of 74 .C and an absolute pressure of 5.20 x 100 Pa. Later, the temperature of the tank has dropped to 35 .C and, due to a leak, the pressure has dropped to 3.90 x 10 Pa. How many grams of chlorine gas have leaked out of the tank? (The mass per mole of Cl2 is 70.9 g/mol.) 9. Suppose a tank contains 690 m3 of neon (Ne) at an absolute pressure of 1.15 x 10 Pa. The temperature is changed from 292 K to 320 K. What is the increase in the internal energy of the neon? J 10. If the temperature of a monoatomic ideal gas is raised from 91 F to 129 F, by how much will the internal energy of 1.50 mol of gas change?1. A gas fills the right portion of a horizontal cylinder whose radius is 5.80 cm. The initial pressure of the gas is 1.01 x 100 Pa. A frictionless movable piston separates the gas from the left portion of the cylinder, which is evacuated and contains an ideal spring, as the figure shows. The piston is initially held in place by a pin. The spring is initially unstrained, and the length of the gas-filled portion is 18.0 cm. When the pin is removed and the gas is allowed to expand, the length of the gas-filled chamber doubles. The initial and final temperatures are equal. Determine the spring constant of the spring. N/m Unstrained spring Pin 2. A spherical balloon is made from a material whose mass is 3.40 kg. The thickness of the material is negligible compared to the 1.30 m radius of the balloon. The balloon is filled with helium (He) at a temperature of 295 K and just floats in air, neither rising nor falling. The density of the surrounding air is 1.19 kg/m3 and the molar mass of helium is 4.0026x1075 kg/mol. Find the absolute pressure of the helium gas. Pa 3. What is the average (rms) speed of the molecules of a helium gas at a temperature of 24C? m/s 4. Calculate the number of gas molecules in a container of volume 0.30 m filled with gas under a partial vacuum of pressure 15 Pa at 17 .C. 5. What is the volume occupied by 4.40 g of hydrogen gas under a pressure of 2.80 atm and a temperature of 20 .C? m 3