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Which of the following pairs does not have similar (same) dimensions?
Checking each pair:
- Tension: $[MLT^{-2}]$ (force). Surface tension: $[MT^{-2}]$ (force per length). These are different — this pair does NOT have the same dimensions.
- Stress and Pressure: both $= [ML^{-1}T^{-2}]$ — same dimensions.
- Planck's constant $[h] = [ML^2T^{-1}]$. Angular momentum $[L] = [ML^2T^{-1}]$ — same dimensions.
- Angle and Strain: both are dimensionless ratios — same dimensions.
Tension $[MLT^{-2}]$ vs Surface tension $[MT^{-2}]$ — these differ by $[L]$, so this pair does NOT have similar dimensions.
The volume occupied by 4.75 g of acetylene gas (C$_2$H$_2$) at 50°C and 740 mmHg pressure is approximately _____ L.
$[R = 0.0826\ \text{L atm K}^{-1}\ \text{mol}^{-1}]$
Molar mass of C$_2$H$_2 = 2(12) + 2(1) = 26\ \text{g/mol}$
Moles $= \dfrac{4.75}{26} \approx 0.1827\ \text{mol}$
$T = 50 + 273 = 323\ \text{K}$
$P = \dfrac{740}{760}\ \text{atm} \approx 0.9737\ \text{atm}$
$V = \dfrac{nRT}{P} = \dfrac{0.1827 \times 0.0826 \times 323}{0.9737} \approx \dfrac{4.875}{0.9737} \approx \mathbf{6}\ \text{L}$
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