Question

The ideal gas law states that PV = NkgT where P is the absolute pressure of a gas, V is the volume it occupies, N is the number of atoms and molecules in the gas, and T is its absolute temperature. The constant ko is called the Boltzmann constant and has the value kg = 1.38x10-23J/K. A very common expression of the ideal gas law uses the number of moles, n- N/NA (NA is Avogadro's number, NA=6.021023 per mole). PV = nRT. The numerical value of Rin Si units is R= 8.31 J/mol-K). Absolute temperature Tin Kelvin) = T (in °C) + 273.15 (a) How many moles of gas are in a bike tire with a volume of 2.00x10 -3 m3 (2.00 L), a pressure of 7.00x105 Pa, and at a temperature of 18 °C? Keep 3 decimal places et (5 attempts remaining) (b) Suppose your bicycle tire is fully inflated, with an absolute pressure of 7.00x105 Pa at a temperature of 18 °C. What is the pressure after its temperature has risen to 35.0°C ? Assume that there are no appreciable leaks or changes in volume. Hint: At first, it may seem that not enough information is given, because the volume V and number of moles n are not specified. What we can do is use the equation twice: Po Vo = nRTO PV = nRTF If we divide Pf Vf by Po Vo we can come up with an equation that allows us to solve for Pt. Report the pressure in 105 Pa. For example, if the pressure is 7.36*105 Pa, just enter 7.36. 1045 PM am (5 attempts remaining) (c) A quantity of an ideal gas is kept in a rigid container of constant volume. If the gas is originally at a temperature of 18 °C, at what temperature (in °C) will the pressure of the gas triple from its base value? Hint: use the stratery similar to (b) (5 attempts remaining) (d) An ideal gas with a fixed number of molecules is maintained at a constant pressure. At 18 °C, the volume of the gas is 1.50 m. What is the volume of the gas when the temperature increases to 75.0°C?

Answer 1

a) use Ideal gas equation, P*V = n*R*T

==> n = P*V/(R*T)

= 7.00*10^5*2*10^-3/(8.314*(18+273.15))

= 0.57936 moles <<<<<<<<-------------Answer

b) at constant volume, P/T = constant

P2/T2 = P1/T1

P2 = (T2/T1)*P1

= ((35 + 273.15)/(18 + 273.15))*7*10^5

= 7.41*10^5 pa <<<<<<<<-------------Answer

c) at constant volume, P/T constant

P1/T1 = P2/T2

T2 = (P2/P1)*T1

= 3*T1

= 3*(18 + 273.15)

= 873.45 K

= 873.45 - 273.15

= 600.3 C <<<<<<<<-------------Answer

d_) at constant pressure,

T/V = constant

T1/V1 = T2/V2

V2 = (T2/T1)*V1

= ((75 + 273.15)/(18+273.15))*1.5

= 1.79 m^3   <<<<<<<<-------------Answer