Question

Please answer all parts of the question: a,b,c,d

Ideal Gas Law The ideal gas law states that PV = Nk T 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 kg is called the Boltzmann constant and has the value kg = 1.38x10-29 J/K. A very common expression of the ideal gas law uses the number of moles, n=N/NA (Nis Avogadro's number, NA = 6.02x104 per mole). PV = nRT. The numerical value of Rin Si units is R= 8.31 J/mol - K). Absolute temperature Tin Kelvin) - Tin °C) + 273.15 m (2.00 L), a pressure of 7.00x10 Pa, and at a temperature of 26 °C? Keep 3 decimal places (a) How many moles of gas are in a bike tire with a volume of 2.00x10 Enter a number mol Submit (5 attempts remaining) (b) Suppose your bicycle tire is fully inflated, with an absolute pressure of 7.00x10 Pa at a temperature of 26 °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 = nRT - If we divide P. V by P. V, we can come up with an equation that allows us to solve for Pp Report the pressure in 10 Pa. For example, if the pressure is 7.36*105 Pa, just enter 7.36. Enter a number 10^5 Pa Submit (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 26 °C, at what temperature (in °C) will the pressure of the gas triple from its base value? Hint: use the stratery similar to (b) Enter a number 'C Submit (5 attempts remaining) (d) An ideal gas with a fixed number of molecules is maintained at a constant pressure. At 26 °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? Enter a number m submit 5 attempts remaining)

Answer 1

(a) Just use ideal gas law

PV = nRT

n = PV / RT

where R is gas constant

n = 7e5 * 2e-3 / 8.314 * (273 + 26)

n = 0.563

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(b) P_f / P_o = T_f / T_o

P_f = (T_f / T_o ) * P_o

P_f = ( 35 + 273 / 26 + 273) * 7e5

P_f = 7.21e5 Pa

(write only 7.21 in the box)

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(c)

here volume is kept constant

so,

T = 3 * T1

T = 3 * (273 + 26)

T = 897 K

or

T = 624 ^oC

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(d)

V_f = ( 1.5 / 299) * 348

V_f = 1.745 m³