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miv72 [106K]
3 years ago
14

Automobile air bags use the decomposition of sodium azide as their sources of gas for rapid inflation, represented in the reacti

on below. What mass (in grams) of NaN3 is required to provide 40.0 L of N2 at 25°C and 763 torr?
Physics
1 answer:
NeTakaya3 years ago
5 0

Answer : The mass of NaN_3 required is 71.175 grams.

Explanation :

To calculate the moles of nitrogen gas, we use the equation given by ideal gas :

PV = nRT

where,

P = Pressure of nitrogen gas = 763 torr

V = Volume of the nitrogen gas = 40.0 L

n = number of moles of gas = ?

R = Gas constant = 62.364\text{ L.torr }mol^{-1}K^{-1}

T = Temperature of helium gas = 25^oC=273+25=298K

Putting values in above equation, we get:

763torr\times 40.0L=n\times 62.364\text{ L.torr }mol^{-1}K^{-1}\times 298K\\\\n=1.642mol

Now we have to calculate the moles of NaN_3.

The balanced chemical reaction is:

2NaN_3(s)\rightarrow 2Na(s)+3N_2(g)

From the balanced chemical reaction, we conclude that

As, 3 moles of N_2 produced from 2 moles NaN_3

So, 1.642 moles of N_2 produced from \frac{2}{3}\times 1.642=1.095 moles NaN_3

Now we have to calculate the mass of NaN_3.

Molar mass of NaN_3 = 65 g/mol

\text{Mass of }NaN_3=\text{Moles of }NaN_3\times \text{Molar mass of }NaN_3

\text{Mass of }NaN_3=1.095mole\times 65g/mole=71.175g

Therefore, the mass of NaN_3 required is 71.175 grams.

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An athlete at the gym holds a 3.0 kg steel ball in his hand. His arm is 60 cm long and has a mass of 3.8 kg, with the center of
Serggg [28]

Answer:

(a) τ = 26.58 Nm

(b) τ = 18.79 Nm

Explanation:

(a)

First we find the torque due to the ball in hand:

τ₁ = F₁d₁

where,

τ₁ = Torque due to ball in hand = ?

F₁ = Force due to ball in hand = m₁g = (3 kg)(9.8 m/s²) = 29.4 N

d₁ = perpendicular distance between ball and shoulder = 60 cm = 0.6 m

τ₁ = (29.4 N)(0.6 m)

τ₁ = 17.64 Nm

Now, we calculate the torque due to the his arm:

τ₁ = F₁d₁

where,

τ₂ = Torque due to arm = ?

F₂ = Force due to arm = m₂g = (3.8 kg)(9.8 m/s²) = 37.24 N

d₂ = perpendicular distance between center of mass and shoulder = 40% of 60 cm = (0.4)(60 cm) = 24 cm = 0.24 m

τ₂ = (37.24 N)(0.24 m)

τ₂ = 8.94 Nm

Since, both torques have same direction. Therefore, total torque will be:

τ = τ₁ + τ₂

τ = 17.64 Nm + 8.94 Nm

<u>τ = 26.58 Nm</u>

<u></u>

(b)

Now, the arm is at 45° below horizontal line.

First we find the torque due to the ball in hand:

τ₁ = F₁d₁

where,

τ₁ = Torque due to ball in hand = ?

F₁ = Force due to ball in hand = m₁g = (3 kg)(9.8 m/s²) = 29.4 N

42.42 cm = 0.4242 m

τ₁ = (29.4 N)(0.4242 m)

τ₁ = 12.47 Nm

Now, we calculate the torque due to the his arm:

τ₁ = F₁d₁

where,

τ₂ = Torque due to arm = ?

F₂ = Force due to arm = m₂g = (3.8 kg)(9.8 m/s²) = 37.24 N

d₂ = perpendicular distance between center of mass and shoulder = 40% of (60 cm)(Cos 45°) = (0.4)(42.42 cm) = 16.96 cm = 0.1696 m

τ₂ = (37.24 N)(0.1696 m)

τ₂ = 6.32 Nm

Since, both torques have same direction. Therefore, total torque will be:

τ = τ₁ + τ₂

τ = 12.47 Nm + 6.32 Nm

<u>τ = 18.79 Nm</u>

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Answer:

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Explanation:

The heat is transferred from one form of energy (friction of the wood being rubbed against the surface) to another (heat energy).

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Answer:

unequal

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Explanation:

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