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v=sqrt((3RT)/(M))
The root-mean-square speed is the measure of the speed of particles in a gas. Root-mean-square speed,
v, can be calculated using the equation shown, where
M is the molar mass of a gas,
R is the molar gas constant, and
T is the temperature. Which of the following equations correctly expresses the molar mass of a gas in terms of root-mean-square speed, temperature, and the molar gas constant?
Choose 1 answer:
(A)
M=((3RT)/(v))^(2)
(B)
M=(3RT)/((v)^(2))
(C)
M=((v)^(2))/(3RT)
(D)
M=(sqrt(3RT))/(v)

$v=\sqrt{\frac{3 R T}{M}}$ $\newline$ The root-mean-square speed is the measure of the speed of particles in a gas. Root-mean-square speed, $v$ , can be calculated using the equation shown, where $M$ is the molar mass of a gas, $R$ is the molar gas constant, and $T$ is the temperature. Which of the following equations correctly expresses the molar mass of a gas in terms of root-mean-square speed, temperature, and the molar gas constant? $\newline$ Choose $1$ answer: $\newline$ (A) $M=\left(\frac{3 R T}{v}\right)^{2}$ $\newline$ (B) $M=\frac{3 R T}{(v)^{2}}$ $\newline$ (C) $M=\frac{(v)^{2}}{3 R T}$ $\newline$ (D) $M=\frac{\sqrt{3 R T}}{v}$

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Volume of cubes and rectangular prisms: word problems

Full solution

Q.

v=\sqrt{\frac{3 R T}{M}}

\newline

The root-mean-square speed is the measure of the speed of particles in a gas. Root-mean-square speed,

v

, can be calculated using the equation shown, where

M

is the molar mass of a gas,

R

is the molar gas constant, and

T

is the temperature. Which of the following equations correctly expresses the molar mass of a gas in terms of root-mean-square speed, temperature, and the molar gas constant?

\newline

Choose

1

answer:

\newline

(A)

M=\left(\frac{3 R T}{v}\right)^{2}

\newline

(B)

M=\frac{3 R T}{(v)^{2}}

\newline

(C)

M=\frac{(v)^{2}}{3 R T}

\newline

(D)

M=\frac{\sqrt{3 R T}}{v}

Square Both Sides: We start with the given equation for root-mean-square speed: $v = \sqrt{(\frac{3RT}{M})}$ . To solve for $M$ , we need to square both sides of the equation to get rid of the square root. $v^2 = \frac{3RT}{M}$
Multiply by M: Next, we multiply both sides by M to get M on one side of the equation by itself. $\newline$ $M \cdot v^2 = 3RT$
Divide by $v^2$ : Now, we divide both sides by $v^2$ to isolate $M$ . $\newline$ $M = \frac{3RT}{v^2}$

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