GO ONLINE Using the Combined Gas Law Using Gay-Lussac's Law (continued Sample Problem F A helium-filled balloon has a volume of 50.0L at 25°C and 1.08 atm. What volume will it have at 0.855 atm and 10.0°C? Solve It! Cards HMHScience.com O SOLVE Substitute known values for T, P, and P, to calculate the new temperature. T, P, 298 K x 6.50 atm - 440 K 4.40 alm Given: V, of He = 50.0 L Convert back to "C. O ANALYZE 440 K= (440 - 273) "C= 167°C T of He = 25°C + 273 = 298 K; T of He = 10°C + 273 = 283 K P, of He = 1.08 atm; P,of He = 0.855 atm O CHECK YOUR WORK The units cancel to give Kelvin temperature, which was converted to "C. The number of significant figures is correct because the data were given to three significant figures. The pressure increases, so the temperature must also increase. Unknown: V,of He O PLAN Because the gas remains at constant pressure, an increase in temperature will cause an increase in volume. To obtain V2, rearrange the equation for Charles's law, Practice 1. At 120.0°C, the pressure of a sample of nitrogen is 1.07 atm. What will the pressure be at 205°C, assuming constant volume? 2. A cylinder of compressed gas has a pressure of 4.882 atm on one day. The next day, the same cylinder of gas has a pressure of 4.690 atm, and its temperature is 8'C. What was the temperature on the previous day in C? 3. A mylar balloon is filled with helium gas to a pressure of 107 kPa when the temperature is 22°C. If the temperature changes to 45°C, what will be the pressure of the helium in the bailoon? PV. P.V. T, P,V,T, PT, 3 SOLVE Substitute the known values to obtain the new volume, V (1.08 atm)(50.0 L He)(283 K) (0.855 atm)(298 K) = 60.0 L He O MAIN IDEA Gas pressure, temperature, and volume are interrelated. 4 CHECK YOUR The pressure factor 1.80/0.855 predicts a larger volume, and the temperature factor 283/298 predicts a smaller volume. The pressure factor predominates, increasing the volume from 50.0 L to 60.0 L. Units cancel appropriately. The answer is correctly expressed to three significant figures. WORK A gas sample often undergoes changes in temperature, pressure, and volume all at the same time. When this happens, three variables must be dealt with at once. Boyle's law, Charles's law, and Gay-Lussac's law can be combined into a single expression that is useful in such situations. The combined gas law expresses the relationship between pressure, volume, and temperature of a fixed amount of gas. The combined gas law can be ex- pressed as follows Practice Ansaers in Appendix E 1 The volume of a gas is 27.5 mlL at 22.0°C and 0.974 atm. What will the volume be at 15.0°C and 0.993 atm? 2.A 700.0 ml gas sample at STP is compressed to a volume of 200.0 ml, and the temperature is increased to 30.0°C. What is the new pressure of the gas in Pa?

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