User:JelloPiranha/Sandbox4

21.
'''The pressure exerted on a 240. mL sample of hydrogen gas at a constant temperature is increased from 0.428 atm to 0.724 atm. What will the final volume of the sample be?'''

$$(240.mLH_2)(0.428atm)=(0.724atm)(x)$$ $$102.72atm mLH_2=0.724x atm$$ $$141.878mLH_2=x$$ $$V_f=142mLH_2$$

26.
'''A sample of air has a volume of 140.0mL at 67°C. At what temperature will its volume be 50.0mL at constant pressure?'''

67°C + 273.15 = 340.15 K → 340. K $$\frac{140.0mL}{340.K}=\frac{50.0mL}{x}$$ $$140.0x mL=17000mL K$$ $$x=121.429K$$ 121.429 K - 273.15 = -151.721°C Tf=-151°C

27.
'''At standard temperature, a gas has a volume of 275mL. The temperature is then increased to 130.°C. and the pressure is held constant. What is the new volume?'''

0°C + 273.15 = 273.15 K → 273 K 130.°C + 273.15 = 403.15 K → 403 K $$\frac{275mL}{273K}=\frac{x}{403K}$$ $$110000mL K=273x K$$ $$405.952381=x$$ $$V_f=406mL$$

28.
'''A sample of hydrogen at 47°C exerts a pressure of 0.329 atm. The gas is heated to 77°C at constant volume. What will its new pressure be?'''

47°C + 273.15 = 320.15 K → 320. K 77°C + 273.15 K = 350.15 K → 350. K $$\frac{0.329atm}{320.K}=\frac{x}{350.K}$$ $$115.15atm K=320x K$$ $$0.360atm=x$$ $$P_f=0.360atm$$

31.
A sample of gas at 47°C and 1.03 atm occupies a volume of 2.20 mL. What volume would this gas occupy at 107°C and 0.789 atm?

47°C + 273.15 = 320.15 K → 320. K 107°C + 273.15 = 380.15 K → 380. K $$\frac{(1.03atm)(2.20mL)}{320.K}=\frac{(0.789atm)(x)}{380.K}$$ $$\frac{2.266atm mL}{320K}=\frac{0.789x atm}{380K}$$ $$861.08atm mL K=252.48x atm K$$ $$3.410mL=x$$ $$V_f=3.41mL$$

34.
'''A sample of oxygen at 40.°C occupies 820. mL. If this sample occupies 1250 mL at 60.°C and 1.40 atm, what was its original pressure?'''

40.°C + 273.15 = 313.15 K → 313. K 60°C + 273.15 = 333.15 K → 333. K $$\frac{(x)(820.mL)}{313.K}=\frac{(1.40atm)(1250mL)}{333.K}$$ $$\frac{820x mL}{313K}=\frac{1750atm mL}{333K}$$ $$273060x mL K=547750atm mL K$$ $$x=2.006atm$$ $$P_i=2.01atm$$