1.)A sample of oxygen took 55 seconds to travel a certain distance. How long would it take for the same number of moles of nitrogen to travel the same distance.
2.) A sample of hydrogen gas traveled 45m in a given amount of time. An unknown gas traveled 7.6m in the same amount of time. What is the formula mass of the unknown gas?
1.
The amount of sample is not given so let's make up one; say 1 l is convenient.
rate O2 = 1L/55 sec
rate N2 - 1L/x sec
(1/55)/(1/x) = sqrt (M2/M1)
M2 = molar mass N2
M1 - molar mass O2.
and do i do the same thing for number 2?
yes. The difference is that you have both rates given and are solving for molar mass of one of the gases.
1.) To determine how long it would take for the same number of moles of nitrogen to travel the same distance as the sample of oxygen, we need to consider their respective velocities.
The velocity of a gas is directly proportional to the square root of the temperature and inversely proportional to the square root of its molar mass. Mathematically, we can express this relationship as:
v ∝ √(T/m)
Where:
v = velocity
T = temperature
m = molar mass
Since we are assuming the temperature and the distance to be constant, we can equate the velocities of oxygen (voxy) and nitrogen (vN2) and solve for the unknown time (tN2) required for nitrogen to travel the same distance:
voxy = vN2
√(T/moxy) = √(T/mN2)
Squaring both sides of the equation, we get:
(T/moxy) = (T/mN2)
Simplifying further:
mN2 = moxy
Hence, it will take the same amount of time for nitrogen to travel the same distance as oxygen because the number of moles remains constant.
2.) To calculate the formula mass of the unknown gas given the distance traveled compared to hydrogen gas, we can use the following equation:
d1/d2 = √(M2/M1)
Where:
d1 = distance traveled by hydrogen gas
d2 = distance traveled by the unknown gas
M1 = formula mass of hydrogen gas (2 g/mol)
Rearranging the equation to solve for M2 (the formula mass of the unknown gas):
M2 = M1 * (d2/d1)^2
Plugging in the given values:
M2 = 2 g/mol * (7.6 m / 45 m)^2
Solving the equation, we find the formula mass of the unknown gas.